Showing $n^3 - n$ is divisible by $6$
62100
Show that $n^3-n$ is divisible by $6$ using induction
2522
Why is $a^n - b^n$ divisible by $a-b$?
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$
117761
When is $\binom{n}{k}$ divisible by $n$?
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
80365
Prove that $n$ is divisible by $6$
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
119152
Proving irreducibility of $x^6-72$
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
120227
Proving $6^n - 1$ is always divisible by $5$ by induction
100892
Proving divisibility of $a^3 - a$ by $6$
1895
How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$