Prove that $a^{2n} -b^{2n}$ is divisible by $a+b$
2522
Why is $a^n - b^n$ divisible by $a-b$?
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
113359
Proving that $x^2 + 4$ is not divisible by $3$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
106847
Proof that $n^3+2n$ is divisible by $3$
144132
The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
111098
Prove $2^{2n} = \sum_{k=0}^{n}\binom{2n+1}{k}$
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
50940
Prove $1^{2007}+2^{2007}+\cdots+n^{2007}$ is not divisible by $n+2$