True or False:
If N > p > q, if p is a multiple of q, and if N divided by p has a remainder of R, then N divided by q would have to have the same remainder as R divided by q.
True. If N divided by p has a remainder of R, if we call the quotient k, then N = p*k + R
Now, suppose we divide that sum by q. Since q is a factor of p, it would also be a factor of p*k, and thus go into that term with no remainder. The only remainder will come from R divided by q.