Q:

Find an n such that the equation $x^2+x=0$ in mod n has 4 solutions

So this is my question and I also have to do it so it has 8 solutions, my problem is that I don't really understand how to approach the problem at all.  Any type of help would be appreciated thanks

A:

Hint: try to show that if $n$ is a product of $r$ distinct primes, then $x^2+x=0$ has $2^r$ solutions mod $n$.

