And I've tried this way, but maybe I'm missing something... but, this is what I got by doing it that way... so far....Now you prove it the other way: Assume a - c = nk and show that this gives a = nx + r and c = ny + s means that r = s.
Since a = nx + r and c = ny + s, than filling it in the equation i want to prove, :
nx + r - ny - s = nk
but... I still don't know how to isolate the r and the s.... the other integers don't cancel out, I can simplify it a little bit, but I'm not sure how much help it would be to put it in this form:
r - s = n(y - x + k)
except for the fact that it resembles the first form, (no with integers but with format) I can't see where to go from here.... *sighs* unless i was able to prove that either n = 0 ( which i didn't think it could be, because it says let n be a positive integer) or I have to prove that y - x + k = 0.....