Question

Sums of powers of elements in a subset and polynomial with $\{-1,0,1\}$ coefficients

score 104 · Answer 1 · 2018-09-10 10:04:53

104

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Sums of powers of elements in a subset and polynomial with $\{-1,0,1\}$ coefficients

Published on 10 Sep 2018 - 10:04

score 336 · Answer 2 · 2026-03-25 17:20:07

336

Views

How to prove this inequality involving the minimum of two chosen numbers

Published on 25 Mar 2026 - 17:20

score 112 · Answer 3 · 2026-03-26 04:34:52

112

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determining every function $f$ defined for positive numbers satisfying $f\big(xf(y)\big)f(y)=f(x+y)$, $f(2)=0$ and $f(x)\ne 0$ for $0\le x<2$

Published on 26 Mar 2026 - 4:34

score 342 · Answer 4 · 2026-03-25 01:40:06

342

Views

P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

Published on 25 Mar 2026 - 1:40

score 1.1k · Answer 5 · 2018-09-12 21:47:13

1.1k

Views

(Puzzle) Find the area of the orange quadrilateral in the given figure

Published on 12 Sep 2018 - 21:47

score 216 · Answer 6 · 2026-03-25 17:35:37

216

Views

Combinatorics contest math question

Published on 25 Mar 2026 - 17:35

score 70 · Answer 7 · 2026-03-25 22:03:08

70

Views

GCD of successive terms

Published on 25 Mar 2026 - 22:03

score 127 · Answer 8 · 2018-09-13 13:49:28

127

Views

An Olympiad question about equality

Published on 13 Sep 2018 - 13:49

score 166 · Answer 9 · 2018-09-14 00:10:53

166

Views

Probability of a vector being in a predefined interval in $\mathbb{R}^{2}$

Published on 14 Sep 2018 - 0:10

score 1.4k · Answer 10 · 2018-09-14 02:45:23

1.4k

Views

Rolling a $6$-sided dice indefinitely until lower than the previous throw

Published on 14 Sep 2018 - 2:45

score 275 · Answer 11 · 2018-09-14 03:49:23

275

Views

Prove that $\frac {x^3}{u}+\frac {y^3}{v} + \frac {z^3}{w}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x^2+y^2+z^2) $

Published on 14 Sep 2018 - 3:49

score 346 · Answer 12 · 2018-09-14 21:28:08

346

Views

what is the sum of the numbers form -100 to 98

Published on 14 Sep 2018 - 21:28

score 1.3k · Answer 13 · 2018-09-15 20:57:01

1.3k

Views

Sequence of positive terms with $\lim a_n=0$ and $ c>0$ such that $|a_{n+1}-a_n|\leq c\cdot a_n^2$.

Published on 15 Sep 2018 - 20:57

score 127 · Answer 14 · 2026-03-25 01:40:04

127

Views

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

Published on 25 Mar 2026 - 1:40

score 167 · Answer 15 · 2018-09-16 20:44:09

167

Views

Putnam and Beyond problem 321

Published on 16 Sep 2018 - 20:44

List Question

Sums of powers of elements in a subset and polynomial with $\{-1,0,1\}$ coefficients

How to prove this inequality involving the minimum of two chosen numbers

determining every function $f$ defined for positive numbers satisfying $f\big(xf(y)\big)f(y)=f(x+y)$, $f(2)=0$ and $f(x)\ne 0$ for $0\le x<2$

P.T. $\frac{1}{a^3(b+c)} +\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)} \ge \frac 32$

(Puzzle) Find the area of the orange quadrilateral in the given figure

Combinatorics contest math question

GCD of successive terms

An Olympiad question about equality

Probability of a vector being in a predefined interval in $\mathbb{R}^{2}$

Rolling a $6$-sided dice indefinitely until lower than the previous throw

Prove that $\frac {x^3}{u}+\frac {y^3}{v} + \frac {z^3}{w}\leq \frac {a^4+b^4}{ab (a^2+b^2)}(x^2+y^2+z^2) $

what is the sum of the numbers form -100 to 98

Sequence of positive terms with $\lim a_n=0$ and $ c>0$ such that $|a_{n+1}-a_n|\leq c\cdot a_n^2$.

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

Putnam and Beyond problem 321

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