"Darrell" <email@example.com> wrote in message news:N6WdnZ5jzfWVgEPbnZ2dnUVZ_r6rnZ2d@giganews.com... > "chuck" <firstname.lastname@example.org> wrote in message > news:email@example.com... >> 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.
Strike that. I don't think that's correct. Those are specific, not general, cases. I yield further advice to those more qualified.