Question

I have to proof that ab mod m = (a mod m)(b mod m) mod m for all integers a and b and for all positive integers m. can anyone give me a hint on how to do this?

Answer 1

So far I have defined: \[a = mq + r\] and \[b = ms + t\] where \[q, r, s, t \epsilon Z\] and 0 <= r < m and 0 <= t < m

Answer 2

Then I can define ab and get a product. Not sure if I can manipulate that with distribution and commutativity
somehow to get the individual pieces?