Non-linear congruence solver (modular arithmetic)

Question

Is there an algorithm that can solve a non-linear congruence in modular arithmetic? I read that such a problem is classified as NP-complete.

In my specific case the congruence is of the form:

x^3 + ax + b congruent to 0 (mod 2^64)

where a and b are known constants and I need to solve it for x.

Answer 1

Look at Hensel's lemma.