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Topic: smallest positive integer
Replies: 12   Last Post: Jan 18, 2008 12:18 AM

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Darrell

Posts: 251
Registered: 12/6/04
Re: smallest positive integer
Posted: Sep 4, 2007 11:05 PM
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"chuck" <noemail@gmail.com> wrote in message
news:fbl522$epb$1@geraldo.cc.utexas.edu...
> 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.

--
Darrell




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