Algebra articles, problems, and puzzles.

What Is Arithmetic?
What Is Algebra?
Arithmetic: Articles and Problems

1. 17 rooks on an 8×8 chessboard
2. 1962 IMO, Problem 2: an inequality with a twist
3. 1=2 via Continued Fractions
4. 3-Colors Tower of Hanoi [Java]
5. 3 glass puzzle [JavaScript]
   • 3 glasses puzzle, second, more general tool [JavaScript]
   • 3 Glasses Problem in Barycentric Coordinates
   • 3 Jugs Problem - A Water Doubling Variant
   • Three Jugs Problem [Java]
   • Two Pails Puzzle [Java]
6. 3-Term Arithmetic Progression
7. A 2-Variable Optimization From a China Competition
8. A 4-variable Inequality from the RMM
9. 4x4 coloring problem
10. 6th European Mathematical Cup (2017), Junior Problem 4
11. A 49^th Degree Challenge
12. A Case for Determinants
13. A Case of Divergence
14. A Clique of Acquaintances
15. A Curious Property of Numbers 3 and 5
16. A Cyclic But Not Symmetric Inequality in Four Variables
17. A Cyclic Inequality by Seyran Ibrahimov
18. A Cyclic Inequality from Math Phenomenon
19. A Cyclic Inequality in Three Variables
20. A Cyclic Inequality in Three Variables II
21. A Cyclic Inequality in Three Variables III
22. A Cyclic Inequality in Three Variables IV
23. A Cyclic Inequality in Three Variables V
24. A Cyclic Inequality in Three Variables VI
25. A Cyclic Inequality in Three Variables VII
26. A Cyclic Inequality in Three Variables VIII
27. A Cyclic Inequality in Three Variables IX
28. A Cyclic Inequality in Three Variables X
29. A Cyclic Inequality in Three Variables XI
30. A Cyclic Inequality in Three Variables XII
31. A Cyclic Inequality in Three Variables XIII
32. A Cyclic Inequality in Three Variables XIV
33. A Cyclic Inequality in Three Variables XV
34. A Cyclic Inequality in Three Variables XVI
35. A Cyclic Inequality in Three Variables XVII
36. A Cyclic Inequality in Three Variables XVIII
37. A Cyclic Inequality in Three Variables XIX
38. An Estimate for the Roots of Quadratic Equation
39. An Exercise in Complex Numbers: Problem 4217 from Crux
40. An Inequality with Constraint XX
41. A Cyclic Inequality in Three Variables XX
42. A Cyclic Inequality in Three Variables XXI
43. A Cyclic Inequality in Three Variables XXII
44. A Cyclic Inequality in Three Variables XXIII
45. A Cyclic Inequality in Three Variables XXIV
46. A Cyclic Inequality in Three Variables XXV
47. A Cyclic Inequality in Three Variables XXVI
48. A Cyclic Inequality in Three Variables And One More
49. >A Cyclic Inequality In Three Variables by Sorin Radulescu
50. A Cyclic Inequality in Three Variables by Uche E. Okeke
51. A Cyclic Inequality from India In Three Variables And More
52. A Cyclic Inequality in Three Variables with Constraint
53. A Cyclic Inequality in Three or More Variables
54. A Cyclic Inequality of Degree Four
55. A Cyclic Inequality With Constraint in Two Triples of Variables
56. A Cycling Inequality with Integrals
57. A Cycling Inequality with Integrals II
58. A Cyclic Inequality with Many Sums
59. A Cyclic Inequality with Powers 2 through 7
60. A Cyclic Inequality in Three Variables with a Variable Hierarchy
61. A Cyclic Inequality on [-1,1]
62. A Diophantine Equation - Problem from 2000 Belarus MO
63. A Diophantine Equation with Square Roots - Problem from the 2008 British MO
64. A DIY Proof of the Irrationality of sqrt(2)
65. A Fancy Sum from the APMO 2000, Problem 1
66. A Few Variants of a Popular Inequality And a Generalization
67. A Formula for sin(3x)
68. A Functional Equation from 1968 IMO
69. A Functional Equation from the 2012 IMO
70. A Generalization of an Inequality from a Romanian Olympiad
71. A Limit of a Sequence
72. A Limit of Another Sequence
73. A Limit of a Series of Determinants
74. A Limit with Fractions, Roots, Powers and Series
75. A Limit With Sums, Roots, And Binomial Coefficients
76. A Little of Algebra for an Inequality, A Little of Calculus for a Generalization
77. A Little More of Algebra for an Inequality, A Little Less of Calculus for a Generalization
78. A Long Cyclic Inequality of Degree 4
79. A Low Bound for 1/2 * 3/4 * 5/6 * ... * (2n-1)/2n
80. A Mathematical Rabbit out of an Algebraic Hat
81. A Memorable Fact
82. A Middle School Problem from a Moscow Olympiad
83. A Moscow Olympiad Question with Two Inequalities
84. A New Proof That the Rationals Are Countable
85. A Not Quite Cyclic Inequality
86. A Not Quite Cyclic Inequality from Tibet
87. A Not Symmetric Inequality [JavaScript]
88. A Not So Simple Inequality in Three Variables
89. A One-Line Proof of the Infinitude of Primes
90. A Partly Cyclic Inequality in Four Variables
91. A Problem for the 2015 New Year's Eve
92. A Problem From a Mongolian Olympiad for Grade 11
93. A Problem from Croatian TST
    • A Problem from Croatian TST, Proof Variants
94. A Problem form the Short List of the 2018 JBMO
95. A Problem from the Danubius Contest 2016
96. A Problem from the Danubius-XI Contest
97. A Problem From the Romanian Mathematical Competitions (2016)
98. A Problem in Complex Numbers Sets 3 Aside
99. A Problem in Division of Polynomials
100. A Problem with a Magical Solution from Secrets in Inequalities
101. A Proof by Game for a Sum of a Convergent Series
102. A Property of Number 4
103. A Property of Product of Special Matrices, Probably Folklore
104. A Property of the fusc() Function
105. A Refinement of Turkevich's Inequality
106. A Representation of Rational Numbers
107. A Quartic Equation
108. A Series with k-Permutations
109. A Simple Inequality with Many Variables
110. A Simple Cyclic Inequality in Three Variables
111. A Simple Inequality in Three Variables
112. A simple integral
113. A simple integral, III
114. A Simple Integral of a Peculiar Function
115. A Simplified Version of Leo Giugiuc's Inequality from the AMM
116. A Sum by Dorin Marghidanu
117. A Sum of a Double Series
118. A System of Equations Begging for Generalization
119. A System of Equations in Determinants
120. A System of Two Equations Replete with Squares
121. A Telescoping Series
122. A Tricky Integral Inequality
123. A Trigonometric Inequality from the RMM
124. >A Trigonometric Observation in Right Triangle
125. A Triple Integral Inequality
126. A True Algebraic-Geometric Inequality
127. A Warmup Inequality from Vasile Cirtoaje
128. ab + bc + ca ≤ aa + bb + cc
129. About numbers
130. Absolute Value
131. Absolute Value and 1998 integers
132. Achieve the Equilibrium [Flash]
133. Addition
     • Addition and Subtraction of Functions [Java]
134. Addition and Subtraction Formulas for Sine and Cosine III
135. Addition and Subtraction Formulas for Sine and Cosine IV
136. Advancing a Millenium Problem [JavaScript]
137. Affirmative Action Problem [Java]
138. Algebraic-Geometric Inequality
139. Algebraic Structure of Complex Numbers
140. All Integers Are Equal to 1
141. All Integers Are Even
142. All Powers of 2 Are Equal to 1
143. All Powers of x are Constant
144. Almost every integer has the digit 3 in it
145. Almost Integers - Gaussian Integers
146. Amazing Mix of Triangular Numbers and Golden Ratio
147. Ambassadors at a Round Table [Java]
148. An Acyclic Inequality in Three Variables
149. An Algebraic Lemma with Geometric Consequences [JavaScript]
150. An Application of Quadratic Formula
151. An Arctan Identity and its Consequence [JavaScript, GeoGebra]
152. An Easy Cyclic Inequality And a Remark
153. An Easy Inequality with Three Integrals
154. An Elementary Inequality by Non-elementary Means
155. An Elementary Proof for Euler's Series
156. An Equation in Determinants
157. An Equation in Factorials
158. An Equation in Matrices
159. An Equation in Radicals
160. An Equation in Reciprocals
161. An Equation in RxR from Romania
162. An Equation in Squares [JavaScript]
163. An Equation Involving Four Collinear Points
164. An Exercise without Calculating Aids
165. An Identity between the Roots of a Cubic Polynomial - Problem from the 2007 Irish MO
166. An Identity From the 2010 China Mathematical Competition
167. An Identity Involving the Integer Part - Problem from the 1981 Canadian MO
168. An Incidental Sum of 24
169. An Increasing Sequence from 2014 IMO
170. An Inequality and Its Modifications
171. An Inequality between AM, QM and GM
172. An Inequality by Uncommon Induction
173. An Inequality for Grade 8
174. An Inequality from a Mongolian Exam
175. An Inequality from the 1967 IMO Shortlist
176. An inequality from 1971 Canadian Mathematical Olympiad
177. An Inequality from Marocco [JavaScript]
178. An Inequality from Tibet
179. An inequality in 2+2 variables from SSMA magazine
180. Inequality in Convex Quadrilateral
181. An Inequality in Determinants
182. An Inequality in Four Weighted Variables
183. An Inequality in Fractions with Absolute Values
184. An Inequality in Integers [JavaScript]
185. An Inequality in Integers II
186. An Inequality in Parallelogram of Unit Area
187. An Inequality in Reciprocals
188. An Inequality in Reciprocals II An Inequality in Reciprocals III
189. An Inequality in Three (Or Is It Two) Variables
190. An Inequality in Triangle and In General
191. An Inequality In Triangle and Without
192. An Inequality In Triangle and Without II
193. An Inequality in Two Or More Variables
194. An Inequality in Two Or More Variables II
195. An Inequality Involving Arithmetic And Geometric Means
196. An Inequality Solved by Changing Appearances
197. An Inequality with Angles and Integers
198. An Inequality with Arbitrary Roots
199. An Inequality with Areas, Norms, and Complex Numbers An Inequality with Central Binomials
200. An Inequality with Complex Numbers of Unit Length
201. An Inequality with Complex Numbers of Unit Length II
202. An Inequality with Cubic Roots
203. An Inequality with Cyclic Sums And Products
204. An Inequality with Cyclic Sums on Both Sides
205. An Inequality with Cyclic Sums on Both Sides II
206. An Inequality with Cyclic Sums on Both Sides III
207. An Inequality with Exponents
208. An Inequality with Five Variables, Only Three Cyclic
209. An Inequality with Fractions
210. An Inequality with Integrals
211. An Inequality with Integrals and Radicals
212. An Inequality with Just Two Variable And an Integer
213. An Inequality with Sines But Not in a Triangle
214. An Inequality with One Tangent and Six Sines
215. An Inequality with Powers And Logarithm
216. An Inequality With Six Variables and Constraints
     • From Six Variables to Four - It's All the Same
217. An Inequality Where One Term Is More Equal Than Others
218. An Inequality with a Parameter and a Constraint
219. An Inequality with Absolute Values
220. An Inequality with an Infinite Series
221. An Inequality with Constraint
222. An Inequality with Constraints II
223. An Inequality with Constraint III
224. An Inequality with Constraint IV
225. An Inequality with Constraint V
226. An Inequality with Constraint VI
227. An Inequality with Constraint VII
228. An Inequality with Constraint VIII [JavaScript]
229. An Inequality with Constraint IX [JavaScript]
230. An Inequality with Constraint X [JavaScript]
231. An Inequality with Constraint XI [JavaScript]
232. An Inequality with Constraint XII
233. An Inequality with Constraint XIII
234. An Inequality with Constraint XIV
235. Inequalities with Constraint XV and XVI
236. An Inequality with Constraint XVII
237. An Inequality with Constraint XVIII
238. An Inequality with Constraint XIX
239. An Inequality with Constraint in Four Variables
240. An Inequality with Constraint in Four Variables II
241. An Inequality with Constraint in Four Variables III
242. An Inequality with Constraint in Four Variables IV
243. An Inequality with Constraint in Four Variables V
244. An Inequality with Constraint in Four Variables VI
245. An Inequality with Cot, Cos, and Sin
246. An Inequality with Cycling Sums
247. An Inequality with Determinants [JavaScript]
248. An Inequality with Determinants II
249. An Inequality with Determinants III
250. An Inequality with Determinants IV
251. An Inequality with Determinants V
252. An Inequality with Determinants VI
253. An Inequality with Determinants VII
254. An Inequality with Exponents [JavaScript]
255. An Inequality with a Generic Proof [JavaScript]
256. An Inequality with Nested Radicals
257. An Inequality via Young's Theorem
258. An Inequality with Just Two Variable
259. An Inequality with Just Two Variable II
260. An Inequality with Just Two Variable III
261. An Inequality with Just Two Variables IV
262. An Inequality with Just Two Variables V
263. An Inequality with Just Two Variables VI
264. An Inequality with Just Two Variable VII
265. An Inequality with Just Two Variable VIII
266. An Inequality with Permutations, I [JavaScript]
267. An Inequality with Permutations, II [JavaScript]
268. An Inequality with Two Cyclic Sums
269. An Inequality with Two Pairs of Triplets An Inequality with Two Triples of Variables
270. An Inequality with Two Triples of Variables II
271. Inequality with Two Variables? Think Again
272. An Inequality with Two Variables from Awesome Math
273. An Infinite Product from Recursion
274. An Integer Root of a Polynomial with Integer Coefficients
275. An Integral Estimate
276. An Integral Identity with Two Functions
277. An Integral from the RMM
278. An Integral Inequality from the RMM
279. An Old Inequality
280. An Unsolvable Riccati Equation
281. An Unusual Quadratic Equation
282. Another Face and Proof of a Trigonometric Identity
283. Another Inequality with Logarithms, But Not Really
284. Another Integral Inequality from the RMM
285. Another Problem from the 2016 Danubius Contest
286. Another Property of Number 4
287. Another simple integral
288. An Unusual Problem by Leo Giugiuc
289. Any Integer with Three 2s
290. Application of Cauchy-Schwarz Inequality
     • An Application of Cauchy-Schwarz Inequality
291. Applications of Schweitzer's Inequality
292. Approximation Of Roots
293. Area of a Circle by Rabbi Abraham bar Hiyya Hanasi [Java]
294. Areas on the Graphs of Power Functions
295. Arithmetic-Geometric Means Inequality
     • AM-GM Inequality
     • An Extension of the AM-GM Inequality
     • An Extension of the AM-GM Inequality: A second look
296. Arithmetic of Pie Sharing
297. Ascending Bases and Exponents in Pascal's Triangle
298. Assigning Numbers to Points in the Plane
299. Associativity from 1977 IMO
300. Averages, Arithmetic and Harmonic Means [Java]
301. Averages in a sequence
302. Ballot Lemma [Java]
303. Banzhaf Power Index Calculator [Java]
304. Barcode Encoding
305. Barcode Magic [Java]
306. Base Converter [JavaScript]
     • Binary System
     • Conversion of Fractions in Various Bases
     • Base (Binary, Decimal, etc.) Converter [Java]
     • e and pi Spoof
     • Expansion of Integers in an Integer Base
307. Bergström's inequality
     • Dorin Marghidanu's Example
     • Dorin Marghidanu's Example II
308. Birth of an Inequality
309. Bayes' Theorem
310. Beatty Sequences
     • Beatty Sequences II
311. Beauty and the Beast - in Trigonometry
312. Bertrand's Postulate
313. Bicubal Domino [JavaScript]
314. Bilateral Diagrams [Java]
315. Binet's Formula via Generating Functions
316. Binet's Formula with Cosines
317. Binomial Distribution [Java]
318. Binomial Theorem
     • Binomial Theorem
319. Bisector of an imaginary angle may be real
320. Brahmagupta-Fibonacci Identity [JavaScript]
321. Byzantine Basketball
322. Calculation of the Digits of pi by the Spigot Algorithm [Java]
     • Calculation of the Digits of pi (Faster Version) [Java]
323. Calculus Proof of the Pythagorean Theorem
324. Candido's Identity
325. Cantor-Bernstein-Schroeder theorem
     • Cantor-Bernstein-Schroeder theorem, a Second Proof
326. Cantor's First Uncountability Proof
327. Cardinal Numbers
328. Cartesian Coordinate System [Java]
329. Cassini's Identity
330. Catalan Numbers in Pascal's Triangle
331. Cavalieri's Principle [Java]
332. Central and Inscribed Angles in Complex Numbers
333. Chebyshev Inequality
334. Chebyshev Holds a Key
335. Check for Negative Roots
336. Chess tournament with 1.5 Points Winners
337. Chinese Remainder Theorem
     • Chinese Remainder Theorem (Pigeonhole principle)
338. Clifford Algebras
339. Clubs in a Vector Space
340. Collatz Conjecture [Java]
341. Coloring a Graph [Java]
342. Coloring Squares, Adding up Numbers
343. Combinatorial Proofs
344. Combo Playground: Calculating the Number of Paths on a Square Grid
345. Committee Chairs
346. Comparing complex numbers
347. Completing a Square and Quadratic Formula
348. Completing the Square Where It Matters
349. Complex Numbers: A Dynamic Tool [Java]
350. Complex number to a complex power may be real
351. Complicated Constraint - Simple Inequality
352. Composition of Functions, an Exercise Constrained Inequality with Reciprocals
353. Constrained Intermarriages [JavaScript]
354. Constructible Numbers
355. Construction of Pascal's Triangle [Java]
356. Constructive Existence of the de Bruijn Cycles
357. Continued fractions
     • Continued Fractions on the Stern-Brocot Tree
358. cos/sin inequality
359. cos(π/7)-cos(2π/7)+cos(3π/7) = 1/2
360. Cospherical Points
361. Countability of Rational Numbers
     • Counting Ordered Pairs
     • Countability of Rational Numbers: PWW
     • Countability of Rational Numbers via Conitnued Fractions
     • Countability of Rational Numbers as a Union of Finite Sets
362. Countability Principle
363. Counting Chips On a Circle [Java]
364. Counting Fat Sets
365. Counting Squares in a Square [Java]
366. Counting Triangles [Java]
367. Counting Triangles II [Java]
368. Covering a Chessboard with a Hole with L-Trominoes [Java]
369. Covering A Chessboard With Domino
     • Dominoes on a Chessboard [Java]
370. Cubes Constrained
371. Cubes in Pascal's Triangle
372. Cubic Equation for the Sides of a Triangle
373. Cubic Formula [JavaScript]
374. Cubics and Bézout's Theorem
375. Cubic Optimization with Linear Constraints
376. Cubic Optimization with Partly Linear Constraints
377. Curious Identities In Pythagorean Triangles
378. Curious Identities Involving Integer Products

     Cute Exercise by Dorin Marghidanu

379. Cyclic Inequality in Four Variables
380. Cyclic Inequality in Four Variables By D. Sitaru
381. Cyclic Inequality in Three Variables by Marian Cucoanes
382. Cyclic Inequality In Three Variables from the 2018 Romanian Olympiad, Grade 9
383. Cyclic Inequality In Three Variables From Vietnam by Rearrangement
384. Cyclic Inequality with Arctangents
385. Cyclic Inequality with Logarithms
386. Cyclic Inequality with Square Roots
387. Cyclic Inequality with Square Roots And Absolute Values
388. Dan Sitaru's Amazing, Never Ending Inequality
389. Dan Sitaru's Cyclic Inequality in Four Variables
390. Dan Sitaru's Cyclic Inequality In One Variable
391. Dan Sitaru's Cyclic Inequality In Many Variables
392. Dan Sitaru's Cyclic Inequality In Three Variables
393. Dan Sitaru's Cyclic Inequality in Three Variables II
394. Dan Sitaru's Cyclic Inequality in Three Variables III
395. Dan Sitaru's Cyclic Inequality in Three Variables IV
396. Dan Sitaru's Cyclic Inequality in Three Variables V
397. Dan Sitaru's Cyclic Inequality in Three Variables VI
398. Dan Sitaru's Cyclic Inequality in Three Variables VII
399. Dan Sitaru's Cyclic Inequality in Three Variables VIII
400. Cyclic Inequality In Three Variables From Kvant
401. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints
402. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints IV
403. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints V
     • Refinement on Dan Sitaru's Cyclic Inequality In Three Variables
404. Dan Sitaru's Exercise with Pi and Ln
405. Dan Sitaru's Inequality: From Three Variables to Many in Two Ways
406. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints II
407. Dan Sitaru's Cyclic Inequality In Three Variables with Constraints III
408. Dan Sitaru's Cyclic Inequality in Three Variables IX
409. Dan Sitaru's Inequality by Induction
410. Dan Sitaru's Cyclic Inequality with a Constraint and Cube Roots
411. Dan Sitaru's Cyclic Inequality with a Constraint and Cube Roots II
412. Dan Sitaru's Inequality with a Double Integral
413. Dan Sitaru's Inequality with Roots and Powers
414. Dan Sitaru's Inequality with Tangents
415. Dan Sitaru's Inequality with Three Related Integrals and Derivatives
416. Dan Sitaru's Integral Inequality with Powers of a Function
417. Dan Sitaru's Sum of a Series
418. Daniel Dan's Optimization in Three Variables
419. Darij Grinberg's Inequality In Three Variables
420. Deceptive Appearances
421. Decimal Sums of Successive Integers
422. Derivatives without Limits
423. Descartes' Rule of Signs
424. Determinant and Divisibility
425. Determinant on a Circle
426. Determinants in Pascal's Triangle
427. Diagonal Argument
428. Diophantine Equations
429. Distance between the Orthocenter and Circumcenter
430. Distance Between Strings [Java]
431. Distance From a Point to a Straight Line [Java]
432. Distance Inequality
433. Distances to Three Points on a Circle
434. Distinct Multisets with the Same Pairwise Sum
435. Divergence of {cos(n)} [JavaScript]
436. Divergence of the Harmonic Series (Details)
437. Divide And Conquer in Cyclic Sums
438. Dividing Loot Fairly
439. Divisibility and Modulo Arithmetic at IMO 2007
440. Divisibility by Powers of 2
441. Dollars in Pockets
442. Doodling on April 1st
443. Dorin Marghidanu's Believe It Or Not
444. Dorin Marghidanu's Calculus Lemma
     • An Inequality with Exponents from a Calculus Lemma
     • An Inequality with Exponents from a Calculus Lemma II
445. Dorin Marghidanu's Cyclic Inequality in Three Variables
446. Dorin Marghidanu's Cyclic Inequality in Three Variables II
447. Dorin Marghidanu's Cyclic Inequality in Three Variables III
448. Dorin Marghidanu's Cyclic Inequality with Constraint
449. Dorin Marghidanu's Inequality in Complex Plane
450. Dorin Marghidanu's Functional Equation
451. Dorin Marghidanu's Inequality in Integer Variables
452. Dorin Marghidanu's Inequality in Many Variables
453. Dorin Marghidanu's Inequality in Many Variables Plus Two More
454. Dorin Marghidanu's Inequality with Constraint
455. Dorin Marghidanu's Inequality with Generalization
456. Dorin Marghidanu's Inequality with Powers and Reciprocals
457. Dorin Marghidanu's Inequality with Radicals
458. Dorin Marghidanu's Light Elegance in Four Variables
459. Dorin Marghidanu's Permuted Inequality
460. Dorin Marghidanu's Spanish Problem Dorin Marghidanu's Sums and Products
461. Dorin Marghidanu's Tribute to Descartes
462. Dorin Marghidanu's Two-Sided Inequality
463. Dot Patterns and Sierpinski Gasket [Java]
     • Arithmetic in Disguise [Java]
464. Dots and fractions [Java]
465. Double and Half Angle Formulas
466. Double Sums by Dorin Marghidanu
467. Ducci Sequences [Java]
468. e in the Pascal Triangle
469. EAN-13 Encoding [Java]
470. Eigenvectors by Inspection
471. Elves and Gnomes [JavaScript]
472. Entry 1.414... in Ramanujan's Notebooks
473. Equation in Permutations
474. Equation in Radicals as a System of Equations
475. Equations of the Staight Line [Java]
476. Equivalence Relations
477. Escape of the Clones
478. Euclid's Algorithm
479. Euclid's Algorithm: An Interactive Illustration [Java]
480. Euler Cycles in Digraph
481. Euler's formula for e^iθ
482. Euler's Function and Congruence Theorem
483. Evolution of Algebraic Symbolism
484. Exercise with Square Spiral [GeoGebra]
485. Existence of the de Bruijn Cycles via Graphs
486. Exponential Inequalities for Means
487. Extension of Euclid's Algorithm
488. Extrema of x^3+y^3+z^3-xyz on the unit sphere
489. Factorial Products
490. Factorials and division
491. Fair Division: Method of Sealed Bids II [Java]
492. Falsity implies anything
493. Farey Series
494. Fermat's Like Equation
495. Fermat's Little Theorem
496. Fermat's Only Published Proof
497. Fibonacci Idendtities with Matrices
498. Fibonacci's Quickies
499. Fibonacci Tilings
500. Filling a Grid with Good Neighbors [Java]
501. Filling an Array with 0s and 1s - and Counting [Java]
502. Filling Pool with Fluids
503. Find Minimum without Calculus
504. Find the Maximum and Minimum of a Function
505. Finding Hamilton Paths and Circuits [Java]
506. Finite Sums of Terms 2^(n-i) i²
507. First 1008 Digits
508. First Geometric Interpretation of Complex Numbers [Java]
509. Five Methods of Apportionment [Java]
510. Five Lattice Points [Java]
511. Five Squares in Complex Numbers [GeoGebra]
512. Fixed Point of a Family of Parabolas
513. Fleury's Algorithm and Euler's Paths and Cycles [Java]
514. Flipping Items Simultaneously [Java]
515. Flipping Items Simultaneously II [Java]
516. Flipping Items Simultaneously III [Java]
517. Flipping pancakes [Java]
518. Floor Function
519. Formal Systems - an Example
520. Formula for Primes
521. Four Hinged Squares: using complex numbers
522. Four Integrals in One Inequality
523. Four Numbers, Six Differences, GCD of the Products
524. Four Pegs That Form a Square
     • Four Pegs That Form a Square [Java]
525. Four Voting Methods [Java]
526. From The Sum of Angles To The Sum of Sines
527. Function
528. Function in the Plane That Vanishes
529. Functional Inequality from Vietnam
530. Fundamental Theorem of Algebra
     • Fundamental Theorem of Algebra - Yet Another Proof
531. Futurama Theorem and Puzzle [Java]
532. Gasoline Stations on a Circular Trek
533. Gauss and Euler Integrals
534. Gauss' Lemma
535. Gauss' theorem on constructibility of regular polygons
536. GCD of Fibonacci Numbers
537. GCD(M, N) × LCM(M, N) = M × N [Java]
538. Generalization That Solves the Problem
539. Generating Functions
     • Generating Functions [Java]
     • Coin Change [Java]
     • Fast Power indices [Java]
     • Weighted Voting and Power Indices [Java]
     • Generating Functions from Recurrences
540. Geometric Construction of Roots of Quadratic Equation [Java]
541. Getting a Scout out of Desert [Java]
542. Getting Your Rightful Share Back [JavaScript]
543. Gheorghe Stoica's Problem from Gazeta Matematica Gireaux's Theorem
544. Gödel's Incompleteness Theorem
545. Golden Ratio is Irrational
546. Graph and Roots of a Third Degree Polynomial [Java]
547. Graph and Roots of Quadratic Polynomial [Java]
548. Graph of a Polynomial [Java]
549. Graph of a Polynomial Defined by Its Roots [Java]
550. Graph with Nodes of Even Degree
551. Graph without 3-Cycles
552. Graphing Equations Is Useful
553. Graphing Equations Is Useful, II [Java]
554. Graphing Equations Is Useful, III
555. Graphing Equations Is Useful, IV
556. Graphing Equations Is Useful, V
557. Greatest Difference in Arithmetic Progression
558. Group multiplication of permutations [Java]
559. 1/2 = 1
560. Hadamard's Determinant Inequalities and Applications I
561. Hadamard's Determinant Inequalities and Applications II
562. Harmonic Serires And Its Parts
563. 2006 Hellenic Mathematical Olympiad, Problem 4 [JavaScript]
564. Hlawka's Inequality
     • An Application of Hlawka's Inequality
     • An Application of Hlawka's Inequality II
     • Hlawka-like Dinca's Inequality
     • Hlawka-like Inequality for Convex Functions
565. Horner's Method [Java]
566. How Jost Burgi Computed the Sines of All Integer Angles in 1586
567. How to Ask an Embarrassing Question
568. How to define a permutation? [Java]
569. How to write an equation of the union of two sets
570. However You Solve It ... A Wonderful Equation
571. Hung Viet's Inequality
572. Hung Viet's Inequality II
573. Hung Viet's Inequality III
574. Hung Viet's Inequality IV
575. Hyperintegers and Hyperreal Numbers
576. Identities with Triangular Numbers
577. Imad Zak's Cyclic Inequality in Three Variables
578. Imad Zak's Cyclic Inequality in Three Variables II
579. Implementation of Base Conversion
580. Importance of the Absolute Value
581. Improving an Inequality [JavaScript]
582. Improving on an Escalator [JavaScript]
583. In Calculus too 1 = 0
584. Inclusion-Exclusion Principle
585. Inclusion-Exclusion Principle: an Example
586. Inequalities and Quadratic Forms
587. An Inequality for Mixed Means
588. An Inequality from RMM with a Generic 5
589. An Inequality from RMM with Powers of 2
590. Inequality 101 from the Cyclic Inequalities Marathon
591. Inequality 1/2·3/4·5/6· ... ·99/100 < 1/10
592. Inequality (1 + 1^-3)(1 + 2^-3)(1 + 2^-3)...(1 + n^-3) < 3
593. Inequality 1 + 2^-2 + 3^-2 + 4^-2 + ... + n^-2 < 2.
594. Inequality by Calculus
595. Inequality for Integer Sequences
596. Inequality for Integer Sequences II
597. Inequality for Mixed Means
598. An Inequality from Gazeta Matematica, March 2016
599. An Inequality from Gazeta Matematica, March 2016 II
600. An Inequality from Gazeta Matematica, March 2016 III
601. An Inequality from Gazeta Matematica, March 2016 IV
602. Inequalities with Double And Triple Integrals
603. Inequality from Math Magazine 2009
604. Inequality from Math Phenomenon
605. Inequality in Acute Triangle
606. Inequality of a Series of Square Roots
607. Inequality with Constraint from Dan Sitaru's Math Phenomenon
608. Inequality with Csc And Sin
609. An Inequality with Exponents [JavaScript]
610. An Inequality with Finite Sums
611. An Inequality with Integrals and Rearrangement
612. Inequality with Logarithms
613. Inequality with Powers And Radicals
614. Inequality with Three Linear Constraints
615. Inequality with Three Numbers, Not All Zero
616. Inequality with Two Minima
617. Infinite Discent for x⁴ + y⁴ = z⁴
618. Infinitesimals. Non-standard Analysis
619. Infinitude of Primes
     • Infinitude of Primes - A Topological Proof
     • Infinitude of Primes - A Topological Proof without Topology
     • Infinitude of Primes Via *-Sets
     • Infinitude of Primes Via Coprime Pairs
     • Infinitude of Primes Via Fermat Numbers
     • Infinitude of Primes Via Harmonic Series
     • Infinitude of Primes Via Lower Bounds
     • Infinitude Of Primes From Legendre's Formula
     • Infinitude of Primes - via Fibonacci Numbers
     • Infinitude of Primes - via Bertrand's Postulate
     • Infinitude of Primes - An Impossible Injection
     • Infinitude of Primes - from Infinitude of Mutual Primes
     • Infinitude of Primes Via Euler's Product Formula
     • Infinitude of Primes Via Euler's Product Formula for Pi
     • Infinitude of Primes - Golomb's Topological Proof
     • Infinitude of Primes Via Powers of 2
     • Infinitude of Primes As a Quickie
     • Infinitude of Primes - A. Thue's Proof
620. Infinity As a Limit
621. Inflection Points of Fourth Degree Polynomials [Java]
622. Inheriting Inequality
623. An innovative recurrence
624. Integer Iterations on a Circle [Java]
     • What Is Your Answer to That Question? [Java]
625. Candy Game (Change Discharged) [Java]
626. Integer Iterations on a Circle III [Java]
627. Integer roots of integers are irrational
628. Integer Triangle That Sums to Cube
629. Integers and Rectangles [Java]
630. Integers and Rectangles: a Proof by Induction [Java]
631. Integers and Rectangles: Two Simple Proofs [Java]
632. Integers With Digits 1 and 2 and Residues Modulo Powers of 2
633. Integral in Normal Distribution
634. Integral Is Area
635. Integrals of a Function And Its Inverse
636. Interest Calculations [Java]
637. Integral of a Piece-wise Function
638. Irrationality of k-th roots
639. Irrationality of sqrt(2) via a Difference Equation
640. Is GLOBALHELLFRY a Prime? [JavaScript]
641. Is the Triangle Inequality Necessary?
642. Is There a Limit?
643. ISBN Encoding [Java]
644. Irrational number to an irrational power may be rational
645. Is 0.999... = 1?
     Is .999... = 1? A Non-standard View
646. It's All About Powers of 10
647. Iterations on Monotone Functions
648. Jensen's Inequality [JavaScript]
649. Ji Chen's Inequality
650. Joachimsthal's Notations
651. Jumping Isn't Everything [Java]
652. Kaprekar's Iterations and Numbers [Java]
653. Kulikowski's Theorem
654. Kunihiko Chikaya's Inequality
655. Kunihiko Chikaya's Inequality with a Constraint
656. Kunihiko Chikaya's Inequality with Parameter
657. Labeling Subsets
658. Lagrange's identity, Proof
659. Lagrange interpolation
660. Lamé's Theorem - First Application of Fibonacci Numbers
661. Langford and Skolem Sequences [Java]
662. Latin Squares [Java]
     • Infinite Latin Squares
     • A Problem on an Infinite Checkerboard
663. Le Khanh Sy's Problem
664. Leech Trees and Taylor's Criterion
665. Legendre's Formula
666. Legendre's Theorem - The Prime Factorization of Factorials
667. Leibniz and Pascal Triangles [Java]
668. Leo Giugiuc and Vasile Cirtoaje's Cyclic Inequality
669. Leo Giugiuc's Cyclic Inequality in Square Roots
670. Leo Giugiuc's Cyclic Inequality in Three Variables
671. Leo Giugiuc's Cyclic Quickie in Four Variables
672. Leo Giugiuc's Cyclic Inequality with a Constraint
673. Leo Giugiuc's Exercise
674. Leo Giugiuc's Inequality with Constraint
675. Leo Giugiuc's Optimization with Constraint
676. Leo Giugiuc's Trigonometric Lemma
677. Less than, Equal to, Greater Than Symbols
678. Lewis Carroll's Game of Logic [Java]
679. Light Bulbs in a Circle [Java]
680. Lights Out [Java]
681. Limit of a Recursive Sequence
682. Linear Algebra Tools for Proving Inequalities
683. Linear Algebra Tools for Proving Inequalities: Cauchy-Binet Formula
684. Linear Function with Coefficients in Arithmetic Progression [GeoGebra]
685. Linear functions
686. Linear Programming
687. Linear System with Parameter
688. Listing All Combinations [Java]
689. Listing all permutations [Java]
690. Listing All Permutations: Johnson-Trotter Method [Java]
691. Logistic Model applet [Java]
692. Long Huynh Huu's Inequality and Solution
693. Long Runs of Composite Numbers
694. Long Up Short Down
695. Looking your best
696. Loop or Halt [Java]
697. Lorian Saceanu's Cyclic Inequalities with Three Variables
698. Lorian Saceanu's Inequality with Many Variables
699. Lucas' Theorem
700. Lucas' Theorem II
701. Lucky Numbers [Java]
702. Marian Dinca's Refinement of Nesbitt's Inequality
703. Marriage Theorem
704. Marriage Problem, simulation [Java]
705. Math Lotto
706. Mathematical Induction
707. Mathematical Proof
708. Mathematicians Doze Off
709. Matrices and Determinants as Optimization Tools: an Example
710. Matrix Groups
711. Maximum Volume of a Cut Off Box [Java]
712. Means [Java]
713. Mediant Fractions
714. Method of Markers II [Java]
715. Michael Rozenberg's Inequality in Three Variables with Constraints
716. Michael Rozenberg's Inequality in Two Variables
717. Minesweeper Theorem
718. Mini Lights Out [Java]
719. Minimax Principle [Java]
720. Minimax Theorem [Java]
721. Minimum of a Cyclic Sum with Logarithms
722. Minimum of Cotangents from Saint Petersburg
723. Minumum Spanning Trees and Kruskal's Algorithm [Java]
724. Minimum under Two Constraints
725. Minus One But What a Difference
726. Modular Arithmetic [Java]
727. Monotone Convergence Theorem
728. Monotone Number Sequences [Java]
729. Monthly Problem 11199
730. Much from Little
731. Muirhead's Inequality
732. Multiplication
733. Multiplication of Points on a Circle [JavaScript, GeoGebra]
734. Multiplication of Points on an Ellipse [JavaScript, GeoGebra]
735. Napoleon's Relatives [Java]
736. Negative on the left, positive on the right: how come?
737. Nested Radicals
738. Nested Subsets
739. New Proof of Euclid's Theorem
740. Newton's Method [Java]
741. Newton's and Maclaurin's Inequalities [JavaScript]
742. Hung Nguyen Viet's Inequality with a Constraint
743. Nine Squares [Java]
744. No Flipping without End [Java]
745. NonSquare Matrix as a Tool for Proving an Inequality
746. Number 8 Is Interesting
747. Number Comparison - from the 1969 Canadian MO
748. Number sequences and Pigeonhole [Java]
749. Number System With Base 36
750. Modern Vietnamese Classic
751. On Dedekind Cuts
752. On the Games of Hex and Y
753. On the Intersection of kx and |sin(x)| [JavaScript]
754. On the Intersection of 1+x and e^x and Trigonometric Consequences [JavaScript]
755. One Dimensional Ants
756. One Inequality - Two Domains
757. One Trigonometric Formula and Its Consequences
758. Optimization in Four Variables with Two Constraints
759. Optimization with Many Variables
760. Order. Well-ordered sets.
761. Order and Chaos in Multiple Pendulums
762. Ordinal Numbers
763. Orthocenter in Complex Plane
764. Outline Mathematics
     • Billy is twice as old as Sally [Java]
     • Coin Counting Word Problem [Java]
     • Crab's Weight [Java]
     • "Math trick" with two dice [Java]
     • Primes as differences of squares [Java]
     • Problem 1 from the 2017 Canada MO
     • Problem 2 from the 2017 Canada MO
     • Problem #24 from the Rhind Papyrus [Java]
     • Robbery #1 [Java]
     • Robbery #2 [Java]
     • Robbery #3 [Java]
     • Robbery #4 [Java]
765. Problem 1 From the 2016 Pan-African Math Olympiad
766. Problem 11867 from the American Mathematical Monthly
767. Problem 2, the 36th IMO (1995)
768. Problem 2 from the 2017 IMO
769. Problem 3824 from Crux Mathematicorum
770. Problem 3980 from Crux Mathematicorum
771. Problem 4002 from Crux Mathematicorum
772. Problem 4010 from Crux Mathematicorum
773. Problem 4020 from Crux Mathematicorum
774. Problem 4033 from Crux Mathematicorum
775. Problem 4117 from Crux Mathematicorum
776. Problem 4142 From Crux Mathematicorum
777. Problem 4165 from Crux Mathematicorum
778. Problem 4186 from Crux Mathematicorum
779. Problem 6 from Dan Sitaru's Algebraic Phenomenon
780. Problem 790 from Pentagon: an Inequality in Two Variables
781. Problem From the 2016 IMO Shortlist
782. Problem M317 from Crux Mathematicorum
783. Proofs of Schweitzer's inequality
784. Prove 2[sqrt(n) - sqrt(n-1)] > 1/sqrt(n)
785. Sam Walters' Four Questions
786. Same Integral, Three Intervals
787. Samuel G. Walters' Congruence
788. Simple Nameless Inequality
789. Small Change Makes Big Difference
790. Smallest multiple of 9 with no odd digits [Java]
791. Snake Permutations And Their Number
792. Solving a Peculiar Third Degree Equation
793. The Basics of Infinite Descent
794. The Joy of Homogeneity
795. The Lucky Find [Java]
796. The Mean Property of the Mean
797. The Number of Judges and the Number of Votes [JavaScript]
798. The power of substitution: solving an equation in a right triangle
799. The power of substitution II: proving an inequality with three variables
800. The power of substitution III: proving an inequality with two variables
801. The Very First Functional Equation at IMO
802. The Very Last, for 2014, proof of the Irrationality of sqrt(2)
803. Three Colors on a Chessboard
804. Three digit twister [Java]
805. Who Has Beard? [Java]
806. Outline Mathematics: Diophantine Equation I [JavaScript]
807. p-adic Expansions
808. p-adic Numbers
809. Pairing Monotone and Convex Functions
810. Parabola and Abutting Equilateral Triangles
811. Parabolic Sieve of Prime Numbers
812. Parity counting [Java]
813. Parrondo Paradox Via Simpson Paradox [Java]
814. Partial But General Case Of Fermat's Last Theorem
815. Party Acquaintances [Java]
816. Patterns in Pascal's Triangle
817. Peano axioms
818. Pennies in Boxes [Java]
819. Percent
820. Permutations
     • Permutations as a Product of Transpositions
     • Counting Permutations with Fixed Points
821. Perrin Sequence
822. Pi in Pascal's Triangle
823. Pi in Pascal's Triangle via Triangular Numbers
824. pi^e vs e^pi [JavaScript]
825. Pigeonhole Principle
     • Pigeonhole Principle and Extensions
826. Pinocchio as Epimenides
827. Place Value [Java]
     • Letter Count in a Sentence [Java]
828. Powers and Fractions Inequality
829. Presence of the Antipodes on a Circle
830. Prime Sums in Pairs
831. Probability of Divisibility
832. Problem 1 from the IMO 2009
833. Problem 11804 from the AMM
834. Problem A1, 69th Putnam Competition
835. Problem A2, 69th Putnam Competition
836. Problem of Divisibility by 5ⁿ
837. Product of Diagonals in Regular N-gon
838. Product Of Four Consecutive Integers
839. Product of Integers that Add Up to 2018
840. Product of Simple Fractions [Java]
841. Product of permutations [Java]
842. Proizvolov's Identity [Java]
843. Proofs Without Words [Java]
844. Property of aⁿ
845. Property of Quadratic Polynomials
846. Property of the Powers of 2 [Java]
847. Puzzlist vs. Mathematician: A Practical Arithmetic Problem
848. Pythagorean Triples [Java]
     • Divisibilty in Pythagorean Triples
     • Pythagorean Triples and Perfect Numbers
     • Pythagorean Triples Calculator [Java]
     • Pythagorean Triples via Fibonacci Numbers
849. Quadratic Function for Solving Inequalities
850. Quadratic Inequalities on [-1,1]
851. An Inequality Where One Term Is More Equal Than Others
852. Quasigroups and block designs from triangular grid [Java]
853. Rabbits Reproduce; Integers Don't
854. Radicals, Radicals, And More Radicals in an Inequality
855. Radon's Inequality and Applications
     • Dorin Marghidanu's Example for Radon's Inequality
856. Ramsey's Number R(3, 3, 3)
857. Ramsey Number R(4, 3)
858. Ramsey Number R(5, 3)
859. Ramsey Number R(4, 4)
860. Ramsey's Theorem
861. Random Walks [Java]
862. Rascal Triangle
863. Rational Solutions to x^y = y^x
864. Rearrangement Inequality [JavaScript]
865. Recombining Permutations [Java]
866. Rectangle on a Chessboard [Java]
867. Rectilinear Paradox
868. Reflection Lemma [Java]
869. Riemann Rearrangement Theorem
870. Riemann Sphere and Möbius Transformation
871. Riemann Sums - Function Integration [Java]
872. Right Replacement [Java]
873. Rolle's and Mean Value Theorems [Java]
874. Rolle's Theorem in Action
875. RomanoNorwegian Inequality
876. Rooks on a Chessboard
877. Roots and Tangents [GeoGebra]
878. Round Robin Tournament
879. Russell's Paradox
880. Solve A Fourth Degree Equation
     • A Followup on Solving A Fourth Degree Equation [JavaScript]
881. Sophie Germain's Identity
882. Square Root of 2 is Irrational, Proof 29
883. Square Roots and Triangle Inequality
884. Squares in Pascal's Triangle
885. Squeeze Theorem
886. Sum of Absolute Values [JavaScript]
887. Sum of All Natural Numbers
888. Sums of Binomial Reciprocals in Pascal's Triangle
889. Squeeze (Sandwich, Pinching ...) Theorem (Lemma): an Example
890. Scalar Product Optimization [JavaScript]
891. Scheduling and Critical Path Algorithm [Java]
892. Schur's Inequality
     • An Application of Schur's Inequality
     • An Application of Schur's Inequality II
893. Scrub Tile Puzzle [Java]
894. Second Pair of Twin Inequalities: Twin 1
895. Second Pair of Twin Inequalities: Twin 2
896. Self-descriptive Strings [Java]
897. Self-documenting Iterations [JavaScript]
898. Self-reference
899. Seven integers under 127 and their Ratios
900. Seven Terms Periodic Sequence
901. Shapley-Shubik Power Index [Java]
902. Shapley-Shubik Power Index Calculator [Java]
903. Shifting Digits and a Point of View
904. Ship-Dock Theorem
     • Ship-Dock Theorem,a formalization
905. Shuttle Puzzle Practice II [Java]
906. Sicherman Dice
907. Sierpinski Gasket and Tower of Hanoi
908. Sierpinski's Gasket and Dihedral Symmetry [Java]
909. Sieve of Squares [Java]
910. Σ2^-n = Σn·2^-n
911. Signs and Sums in a Sequence [Java]
912. Signs in a Matrix [Java]
913. Simple But Uncommon Equation from 1968 IMO
914. Simple Cellular Automaton [Java]
915. Simple Graph Practice [Java]
916. Simple Inequality with a Variety of Solutions
917. Simple Inequality with Many Faces And Variables
918. Simple Somos Sequence - a Russian Olympiad problem
919. Simple Somos Sequence Calculator [Java]
920. Simple Yet Uncommon Inequalities with Absolute Value
921. Simpson Paradox [Java]
922. $\sin 1^{\circ}+\sin {2^\circ}+\sin 3^{\circ}+\cdots+\sin 180^{\circ}=\tan 89.5^{\circ}$
923. Sine And Cosine Are Continuous Functions
924. Sine of a Sum Formula, Proof Without Words
925. Single formula to express any integer with digits 0-9 each used just once
926. Sitaru-Schweitzer Inequality
927. Six Balls, Two Weighings
928. Size of a Class: Two Viewpoints
929. Sladjan Stankovik's Inequality In Four Variables
930. Sladjan Stankovik's Inequality With Constraint
931. Sladjan Stankovik's Inequality With Constraint II
932. Slider Puzzles [Java]
933. Solitaire in Two Colors [Java]
934. Solutions of F(x)=x and F(F(x))=x [JavaScript]
935. Solve - an Olympiad Problem - in Your Mind
936. Solve x^x3 = 3
937. Solve cos²x + cos²2x + cos²3x = 1
938. Solving an Equation with Inverse Functions
939. Soriteses
940. Sorting Algorithms
941. Sperner's Theorem
942. Splitting piles
943. Square Root of 2 as a Continued Fraction
944. Square root of 2 is irrational
945. Star of David Theorems in Pascal Triangle
946. Stars in Array
947. Steinhaus' Problem [Java]
948. Step into the Elliptic Realm
949. Stern-Brocot Tree
950. Straight Tromino on a Chessboard [Java]
951. Structure of Hyperreal Numbers
952. Subsets and Intersections
953. Subtraction Game [Java]
954. Sums of the Elements of Three Element Subsets [JavaScript]
955. Sum of Three Squares [JavaScript]
956. Sums and Products, a Generalization
957. Sums, Products, and 1-1 Functions
958. Sums of Geometric Series - Proofs Without Words [Java]
959. Sums of Power Series
960. Sums Of Successive Squares
961. Sum without Adding
962. Sums and Products [Java]
963. Sums of powers of digits [Java]
964. Superposition Principle
965. Surreal Numbers
966. Swapping Rows and Columns [Java]
967. Sylvester's Problem
     • Sylvester's Problem, a Second Look
968. Taking Games Seriously [Java]
969. Tangential Chaos
970. Telescoping Cubes
971. Telescoping Squares
972. Telescoping Sums and Series [JavaScript]
973. Telescoping Tangents
974. The ass and the mule [Java]
975. The Averages of Sides and Angles in a Triangle
976. The Basic Rules of Counting
     • Example: A Poker Hand
977. The Local-Global Principle
978. The Regula Falsi - Iterated
979. The Roads We Take
980. The Size is in the Eyes of the Beholder
981. Three Complex Numbers Satisfy Fermat's Identity For Prime Powers
982. Three Dimensional Cross
983. Three Junior Problems from Vietnam
984. Three Variables, Three Constraints, Two Inequalities (Only One to Prove) - by Leo Giugiuc
985. Tool for Constructing Orthogonal Latin Squares [Java]
986. Tower of Hanoi, the Hard Way [Java]
987. Train on Bridge [JavaScript]
988. Tran Hoang Nam's Cyclic Inequality in Three Variables
989. Transpositions
990. Traveling Salesman Problem [Java]
991. Treatise on Arithmetical Triangle
992. Triangular numbers that are also square
993. Trigonometric Identity for the Pi Day
994. Trigonometric Inequality with Integrals
995. A Trigonometric Inequality with Ordered Triple of Variables
996. Trilateral Diagrams [Java]
997. Trinary Tree(s) underlying Primitive Pythagorean Triples
998. Tromino Puzzle: Deficient Squares [Java]
999. Twenty five boys and twenty five girls around a table.
1000. Twin Inequalities in Four Variables: Twin 1
1001. Twin Inequalities in Four Variables: Twin 2
1002. Two Constraints, One Inequality by Qing Song
1003. Two Circles and a Limit [Java]
1004. Two Colors in Two Rows [Java]
      • Two Colors in Two Rows II [Java]
1005. Two Cyclic Inequalities [JavaScript]
1006. Two Equations in Three Variables [JavaScript]
1007. Two Men of Tibet [Java]
1008. Two-Parameter Solutions to Three Almost Fermat Equations
1009. Two-Sided Inequality by Dorin Marghidanu
1010. Two Problems by Kunihiko Chikaya
1011. Two Problems from a Serbian 7 Grade Math Competition
1012. Two Products: Constraint and Inequality
1013. Two Sequences Defined by Recurrence
1014. Two-Sided Inequality - One Provenance
1015. Two Solutions: One Correct, One Illuminating. An Example
1016. Uncountability of the Reals - via a Game
1017. Undefined vs Indeterminate in Mathematics
1018. (Un)fair Division by Consensus
1019. Universal Coloring [Java]
1020. Universal Product Code [Java]
1021. Unproperty of the Powers of 2
1022. Unsolved Problem from Crux Solved
1023. USA 1975 Problem 3
1024. Vasile Cirtoaje's Cyclic Inequality with Three Variables
1025. Vandermonde's Convolution Formula
1026. Vandermonde Determinant
1027. Venn Diagrams
1028. Viète's Formulas
      • Venn Diagrams I [Java]
      • Venn Diagrams II [Java]
1029. Voronoi Diagram [JavaSCript]
1030. Ways To Count
1031. Weierstrass Product Inequality
1032. Weierstrass Substitution
1033. What, how, and the Web [Java]
1034. What 1, 6, and 14 Have to Do with 5?
1035. What Is Algorithm?
1036. What Is Determinant?
1037. What Is Finite?
1038. What Is Infinite Descent?
1039. What Is Infinity?
1040. What Is Limit?
1041. What is so natural about "natural logarithms"?
1042. What Is Space Completion?
1043. WHEN THE COUNTING GETS TOUGH, THE TOUGH COUNT ON MATHEMATICS
      • Matrices Help Relationships
      • An Airline Problem
1044. When Two Segments Intersect? [JavaScript]
1045. Where To Start? [Java]
1046. White and Black Balls in Urn. 1 in, 2 out. What Color Remains?
1047. Why 17?
1048. Why Can't They Be All Different?
1049. Why sin(x)/x tends to 1
1050. Why The Number of Primes Could Not Be Finite?
1051. Wilson's Theorem
      • Geometric Proof of Wilson's Theorem
1052. Without Definitions: Why $\displaystyle\frac{1}{3}+\frac{2}{5}=\frac{11}{15}?$
1053. Wonderful Inequality on Unit Circle
1054. Word Problems [Java]
1055. Wu's Inequality
1056. $x_n=\sin 1+\sin 3+\sin 5+\cdots+\sin (2n-1)$
1057. Yet Another Puzzle with Hats
1058. Yet Another Simple Integral
1059. Zeros and Nines [Java]

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