Fermat's Little Theorem/Examples/12 Divides n^2-1 if gcd(n, 6)=1

Examples of Use of Fermat's Little Theorem
$12$ Divides $n^2-1$ if $\gcd \set {n, 6} = 1 \implies 12 \divides n^2 - 1$

Proof
Then:

So we have: