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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 5, 2007 7:13 PM
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"Michael J Hardy" <mjhardy@mit.edu> wrote in message
news:46ded55f$0$483$b45e6eb0@senator-bedfellow.mit.edu...
> Darrell (dr6583@comcastsnip.net) wrote:
>

>> 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.

>
>
> That is nonsense. You can't just "let |a - b| = 1.
> a and b are given. The answer depends on them.
>
> E.g., if a = 20 and b = 3, then a - bk = 20 - 3k. In that case,
> the integers of the form a - bk are those of the form 20 - 3k,
> namely 20, 17, 14, 11, 8, 5, 2, -1, -4, ... etc. (and also 23, 26,
> 29,...). The smallest positive integer among those is 2, and the
> value of k that achieves it is 6.
>
> The answer depends on a and b, so you've got to say what function
> of a and b it is (I've given the answer in only one case). -- Mike Hardy
>
>



Perhaps you should read the rest of the thread where I already retracted my
response.

--
Darrell




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