24 divides Square of Odd Integer Not Divisible by 3 plus 23

Theorem
Let $a \in \Z$ be an integer such that:
 * $2 \nmid a$
 * $3 \nmid a$

where $\nmid$ denotes non-divisibility.

Then:
 * $24 \divides \paren {a^2 + 23}$

where $\divides$ denotes divisibility.