GP has a very convenient function polrootsmod which gives the roots of a polynomial mod a prime. Is there a way to find -- or just count -- the roots of a polynomial mod a composite with a known factorization?
With squarefree moduli this is simple -- count the solutions mod each prime and multiply, or find the solutions mod each and CRT back together if you want each solution. So I guess the question is just about handling prime powers.
Charles Greathouse
Case Western Reserve University