To prove that $(a^n-b^n) \nmid (a^n+b^n)$
12694
Why does $a^n - b^n$ never divide $a^n + b^n$?
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
139718
Prove $6 \nmid [\left( \sqrt[3]{28} - 3 \right)^{-n}]$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
78144
How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
29462
Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$