Prove that ${n^5 - n}$ is divisible by 5
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
80365
Prove that $n$ is divisible by $6$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
29874
Not divisible by $2,3$ or $5$ but divisible by $7$
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
101927
Induction: Prove that $4^{n+1}+5^{2 n - 1}$ is divisible by 21 for all $n \geq 1$.
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
1507
The product of $n$ consecutive integers is divisible by $n$ factorial
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
87666
Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
104965
Find $n$ such that polynomial is divisible
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime