Category:Square Modulo 24 of Odd Integer Not Divisible by 3

This category contains pages concerning Square Modulo 24 of Odd Integer Not Divisible by 3:

Let $a \in \Z$ be an integer such that:

$2 \nmid a$

$3 \nmid a$

where $\nmid$ denotes non-divisibility.

Then:

$a^2 \equiv 1 \pmod {24}$

That is:

$24 \divides \paren {a^2 - 1}$

where $\divides$ denotes divisibility.