Is there a general methodology to solve $X^2 = X \:\mathbb{mod}\: n$?
A solution verifies the interesting fact that $X^i = X \:\mathbb{mod}\: n$ for $i>0$.
I think we can't really use discriminant like in algebra, but there may be a theorem answering my question.
Bonus question: Same with quadratic forms $X^2 + AX + B = 0 \:\mathbb{mod}\: n$