Solve the equation `a*x == b` with Int32 arithmetics
Python 3, 39 bytes



lambda a,b,h=2**31:(a**~-h*b+h)%(2*h)-h


This is a theoretical solution that will take a long time unless a = 1. It uses the Euler-Fermat theorem to determine the modular inverse of a.

Alternate version, 47 bytes

lambda a,b,h=2**31:(pow(a,h-1,2*h)*b+h)%(2*h)-h


This does exactly the same, but in a more efficient manner.

Try it online!