List questions from contest-math

Published on 10 May 2026 - 18:58

107

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For how many values of $x$ in $0 \le x < 2\pi$ does $\frac{\sin(5x)}{\sin(x)} - \frac{\cos(5x)}{\cos(x)}=2$?

Published on 16 Apr 2026 - 20:05

570

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Killing Flies with a Checkerboard Flyswatter

Published on 10 May 2026 - 12:32

621

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finding sum of entries in magic square directly

Published on 10 May 2026 - 13:08

152

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Ratio of the area of a triangle and the area of a square containing it

Published on 15 Apr 2026 - 13:06

180

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Question from the British Mathematical Olympiad

Published on 05 May 2026 - 4:12

1.3k

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A solution using 'Lifting the exponent' lemma to IMO 1990 P3

Published on 15 Apr 2026 - 1:06

115

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Circular geometry problem

Published on 10 May 2026 - 14:02

66

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Prove that for any $a, b, c>0$ we have:

Published on 16 Apr 2026 - 3:39

124

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Tricky Contest Problem

Published on 12 Apr 2026 - 7:39

69

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Let $x, y, z>0$. Prove that $\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y}+\left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$

Published on 15 Apr 2026 - 23:50

411

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$n,p \in \mathbb{N}$ , $p$ prime and $1+np$ perfect square $\implies n+1$ is the sum of $p$ perfect squares.

Published on 10 May 2026 - 15:25

203

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Putnam 1957, 17th Problem

Published on 14 Apr 2026 - 12:20

284

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New strategy for proving an inequality

Published on 10 Apr 2026 - 7:15

159

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If $a^3+b^3=c^3,$ prove that

Published on 15 Apr 2026 - 18:44

List Question

Evaluate $(-\sqrt3 + i)^9$

For how many values of $x$ in $0 \le x < 2\pi$ does $\frac{\sin(5x)}{\sin(x)} - \frac{\cos(5x)}{\cos(x)}=2$?

Killing Flies with a Checkerboard Flyswatter

finding sum of entries in magic square directly

Ratio of the area of a triangle and the area of a square containing it

Question from the British Mathematical Olympiad

A solution using 'Lifting the exponent' lemma to IMO 1990 P3

Circular geometry problem

Prove that for any $a, b, c>0$ we have:

Tricky Contest Problem

Let $x, y, z>0$. Prove that $\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y}+\left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$

$n,p \in \mathbb{N}$ , $p$ prime and $1+np$ perfect square $\implies n+1$ is the sum of $p$ perfect squares.

Putnam 1957, 17th Problem

New strategy for proving an inequality

If $a^3+b^3=c^3,$ prove that

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