Existence of Number to Power of Prime Minus 1 less 1 divisible by Prime Squared/Examples/3

Example of Existence of Number to Power of Prime Minus 1 less 1 divisible by Prime Squared
The smallest positive integer $n$ greater than $1$ such that:
 * $n^{3 - 1} \equiv 1 \pmod {3^2}$

is $8$.

Proof
Only positive integers coprime to $3$ need be checked.

We have that $3^2 = 9$.

Thus: