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.