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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 11:32 PM
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"Darrell" <dr6583@comcastsnip.net> wrote in message
news:N6WdnZ5jzfWVgEPbnZ2dnUVZ_r6rnZ2d@giganews.com...
> "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.


Strike that. I don't think that's correct. Those are specific, not
general, cases. I yield further advice to those more qualified.

--
Darrell




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