I am solving a discrete logarithm problem $\mod N$ where $N$ is composite number, and I found its factors - lots of small primes and two big primes ($> 2^{50}$).
Does the factorization of $N$ somehow help me? I think I could compute the logarithm modulo each prime and then combine it, but do not know how exactly. Seems similar like problems for Chinese remainder theorem but I cannot find the way how to do it.