Is $a^n+b^n$ is divisible by $a+b$?
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
117761
When is $\binom{n}{k}$ divisible by $n$?
80365
Prove that $n$ is divisible by $6$
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
106847
Proof that $n^3+2n$ is divisible by $3$
43113
Whether the given number is divisible by 24?
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
27798
Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
12134
divisibility question in abstract algebra over a field
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
105180
When does $(ab)^n = a^n b^n$ imply a group is abelian?
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
48211
When is $(a+b)^n \equiv a^n+b^n$?