How do I prove that $6 \mid n^3- n$ for all $n ≥ 1$?
62100
Show that $n^3-n$ is divisible by $6$ using induction
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
55273
Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$
77579
Proof by induction that $ 169 \mid 3^{3n+3}-26n-27$
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
122711
Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
77383
Prove that $n^3=n \text{ mod }6$ for every integer $n$.
15210
Group of order 6 proof
118574
prove that $24 \mid a(a^2-1)$
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
62732
Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$.
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
124240
Inductive proof of $\,9 \mathrel| 4^n+6n-1\,$ for all $\,n\in\Bbb N$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
19701
Prove $5\mid2^{4n}-1$ by induction