Thought Process

Clearly, the Chinese Remainder Theorem will be involved in this problem, one difference is we need to account for non-coprime moduli. The CRT wiki contains a section on this, so I just implemented the given algorithm, in order to do this I had to implement the standard Extended Euclidean Algorithm to get the Bezout coefficients, I'm surprised I haven't had to do this yet.

Then, I just implemented my standard Totient Sieve so that I wouldn't have to recalculate phi values and ran through all the possible values with my new Generalized CRT algorithm.

All of these functions have been added to my mathematical Library mathslib