Polynomial congruences

Polynomial Congruences are congruences in the form

$f(x) \equiv 0 \pmod {m}$

where $f(x)$ is an arithmetic function and a polynomial whose range is the integers and $m$ is an integer.

Solving

There are a few ways of solving polynomial congruences, and special cases can make it easier.

Some polynomial congruences can be solved obviously. For example, the congruence

$16x^2 \equiv 13 pmod {192}$

obviously have no solution, since $\gcd (16,192)$ don't divide $13$ .

Additionally, if $f(x)$ is of