Square Modulo 3/Corollary 3

Corollary to Square Modulo 3
Let $n \in \Z$ be an integer such that:
 * $3 \nmid n$

where $\nmid$ denotes non-divisibility.

Then:
 * $3 \divides n^2 - 1$

where $\divides$ denotes divisibility.

Proof
From Square Modulo 3:


 * $3 \equiv 0 \pmod 3 \iff 3^2 \equiv 0 \pmid 3$

Hence also from Square Modulo 3:


 * $3 \not \equiv 0 \pmod 3 \iff 3^2 \equiv 1 \pmid 3$

That is: $3 \nmid n \iff 3 \divides n^2 - 1$