Question

Find the maximum of the value $c(n)$ similar to Hardy's inequality

score 311 · Answer 1 · 2018-11-01 08:00:20

311

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Find the maximum of the value $c(n)$ similar to Hardy's inequality

Published on 01 Nov 2018 - 8:00

score 202 · Answer 2 · 2026-03-26 17:33:41

202

Views

Find all primes $p$ and $q$ such that $p^2+1 | 2003^q+1$ and $q^2+1 |2003^p+1$.

Published on 26 Mar 2026 - 17:33

score 1.1k · Answer 3 · 2026-03-26 09:27:01

1.1k

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Find all functions such that $f(x^2+y^2f(x))=xf(y)^2-f(x)^2$

Published on 26 Mar 2026 - 9:27

score 425 · Answer 4 · 2026-03-26 09:21:47

425

Views

Prove that $f$ is additive if $f(x)f(x-y)+f(y)f(x+y)= f(x)^2+f(y)^2$

Published on 26 Mar 2026 - 9:21

score 262 · Answer 5 · 2018-11-03 23:29:18

262

Views

Surface Area Problem Math Contest

Published on 03 Nov 2018 - 23:29

score 294 · Answer 6 · 2018-11-03 23:31:36

294

Views

How many ways to place three distinguishable tokens on the white spaces of a $4$-by-$4$ chess board?

Published on 03 Nov 2018 - 23:31

score 146 · Answer 7 · 2018-11-04 13:41:34

146

Views

Coloring the all the natural numbers upto $n$

Published on 04 Nov 2018 - 13:41

score 273 · Answer 8 · 2018-11-04 22:17:55

273

Views

On existence of positive integer solution of $\binom{x+y}{2}=ax+by$

Published on 04 Nov 2018 - 22:17

score 129 · Answer 9 · 2018-11-05 10:01:24

129

Views

If $a=b+c$ prove that $S=a^4+b^4+c^4$ is twice the square of a positive integer

Published on 05 Nov 2018 - 10:01

score 494 · Answer 10 · 2026-03-25 19:12:03

494

Views

How many ways 3 persons A, B , C can be put in a row of six empty chair such that A nd B don't sit together

Published on 25 Mar 2026 - 19:12

score 217 · Answer 11 · 2018-11-06 13:56:34

217

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If $x_1, x_2$ are roots of $P(x)=x^2-6x+1$, prove that $5 \nmid x_1^n+x_2^n$

Published on 06 Nov 2018 - 13:56

score 185 · Answer 12 · 2018-11-07 01:35:06

185

Views

Prove that $\sqrt[3]{\frac{1}{9}}+\sqrt[3]{-\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}$ is a root for $x^3+\sqrt[3]{6}x^2-1$

Published on 07 Nov 2018 - 1:35

score 152 · Answer 13 · 2018-11-08 20:55:23

152

Views

The greatest $M$ that $\sqrt[5]{\frac{a}{b+c}}+\sqrt[5]{\frac{b}{c+d}}+\sqrt[5]{\frac{c}{d+e}}+\sqrt[5]{\frac{d}{e+a}}+\sqrt[5]{\frac{e}{a+b}}>M$

Published on 08 Nov 2018 - 20:55

score 97 · Answer 14 · 2026-03-25 03:16:38

97

Views

Inequality using Jensen

Published on 25 Mar 2026 - 3:16

score 102 · Answer 15 · 2018-11-09 17:38:31

102

Views

A prime divisor in a second order recurrence

Published on 09 Nov 2018 - 17:38

List Question

Find the maximum of the value $c(n)$ similar to Hardy's inequality

Find all primes $p$ and $q$ such that $p^2+1 | 2003^q+1$ and $q^2+1 |2003^p+1$.

Find all functions such that $f(x^2+y^2f(x))=xf(y)^2-f(x)^2$

Prove that $f$ is additive if $f(x)f(x-y)+f(y)f(x+y)= f(x)^2+f(y)^2$

Surface Area Problem Math Contest

How many ways to place three distinguishable tokens on the white spaces of a $4$-by-$4$ chess board?

Coloring the all the natural numbers upto $n$

On existence of positive integer solution of $\binom{x+y}{2}=ax+by$

If $a=b+c$ prove that $S=a^4+b^4+c^4$ is twice the square of a positive integer

How many ways 3 persons A, B , C can be put in a row of six empty chair such that A nd B don't sit together

If $x_1, x_2$ are roots of $P(x)=x^2-6x+1$, prove that $5 \nmid x_1^n+x_2^n$

Prove that $\sqrt[3]{\frac{1}{9}}+\sqrt[3]{-\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}$ is a root for $x^3+\sqrt[3]{6}x^2-1$

The greatest $M$ that $\sqrt[5]{\frac{a}{b+c}}+\sqrt[5]{\frac{b}{c+d}}+\sqrt[5]{\frac{c}{d+e}}+\sqrt[5]{\frac{d}{e+a}}+\sqrt[5]{\frac{e}{a+b}}>M$

Inequality using Jensen

A prime divisor in a second order recurrence

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