Show that $\left(2^{xy}-x\right)|\left(x^y-2^{xy^2}\right)$ for $\left(y=1\:\wedge \:x\ge 3\right)\vee \left(y\ge 2\:\wedge \:x\in \mathbb{N}\right)$
2522
Why is $a^n - b^n$ divisible by $a-b$?
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
73892
Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction
82961
Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
16109
Prove that $ \int _a^b\:f\left(x\right)\:\:dx\:=\:\int _a^b\:f\left(a+b-x\right)\:\:dx $
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
96366
show that for any n $\in$ $\Bbb N$ , if n $\ge$ 2, then $\prod_\limits{i=2}^n $ $\left( 1-\frac{1}{i^2}\right)$ = $\frac{n+1}{2n}$
118018
Show $ (n+1)^{1/3}-n^{1/3}=O\left(n^{-2/3}\right) $
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$