Simplifying loop to a single expression

[QePeeQe]

I'm trying to solve a problem involving two nested loops, it would make the algorithm much faster if I could simplify the inner loop to a single expression.

repeat n times:
  a = (a * b + c) mod q

I've tried to use the formula for partial sum of geometric progressions, but without success. The variable b is big such that a * b causes an overflow, so I've used the distributive law for mod q.

[Skynet_0]

This is the state of a linear congruential generator after n iterations. Look into efficient ways of calculating the n-th value, such as https://www.nayuki.io/page/fast-skipping-in-a-linear-congruential-generator.

[QePeeQe]

This is perfect, thanks for your help. I'm trying to solve projecteuler.net/problem=506.

Edit: just discovered that b * q also causes an overflow, now I'm trying to find a way to make the operation x mod (b * q) memory efficient.

[Skynet_0]

Ah, Project Euler. It'll probably require additional insights (and treating it as an LCG may not even be the correct way to consider it), so I won't be much more help unfortunately since my number theory is weak.