Find all solutions of the congruence x^2 + 6x − 31 = 0 (mod 72).
Okay, I’ve tried the problem myself and found that it’s not very straightforward (I believe it’s because the modulus is not a prime). Here’s my solution.
where It is clear that must be even so let
Again we see that must be even, say
Trying in turn, we find that are the only solutions between 1 and 8. Hence the general solution is
Maybe someone has a neater solution?