# user26486

Top Questions

## Prove that if $x_1,x_2,\ldots,x_n>0$, then $(1+x_1)(1+x_1+x_2)\ldots(1+x_1+x_2+\ldots+x_n) \ge \sqrt{(n+1)^{n+1}}\sqrt{x_1x_2\ldots x_n}$.

asked Dec 22 '13 at 15:01

## Find all $x,y,z\in\mathbb N$, $x,y,z>1$ such that satisfy $x\mid yz+1$, $y\mid xz+1$, and $z\mid xy+1$

asked Jan 17 '14 at 21:09

## Prove that there are no such different positive numbers that satisfy both $a+b=c+d$ and $a^3+b^3=c^3+d^3$.

asked Dec 12 '13 at 18:23

## No confirmation pop up when deleting comments (Android app)

asked Feb 8 '15 at 4:53

## $a,b,n,d\in \mathbb N$. $a,b,d$ are different numbers from the interval $(n^2;n^2+n)$. Prove that it can't be true that $d|ab$.

asked Dec 22 '13 at 17:07

## If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.

asked Dec 22 '13 at 23:45

## If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.

asked Dec 28 '13 at 0:52