"chuck" <email@example.com> wrote in message news:firstname.lastname@example.org... > Hi, > I am taking a number theory class right now and this is the first math > class I have taken in quite some time. I just looking for a way to start > this problem. > > show that if a and b are positive integers, then there is a smallest > positive integer of the form > a - bk, k is element of Integers > > So, I guess i don't quite understand what the smallest positve integer > has to do with a and b in this case, or how they are related. my thought > is that k should equal 1 .
Consider a=b. Check the wording of the problem.
For argument sake I will assume a!=b. Since the smallest positive integer is 1, you can always make a-bk=1 by letting |a-b|=1 and |k|=1. IOW, a=b+1 or b=a+1 with k=+/- 1 accordingly.