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Topic: number problem
Replies: 30   Last Post: Jul 3, 2013 12:08 AM

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Timothy Murphy

Posts: 657
Registered: 12/18/07
Re: number problem
Posted: Jun 23, 2013 6:01 AM
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mathguy wrote:

> Can anyone prove the following:
> let S be a set of distinct integers with the property that
> (a-b)^2 divides ab for distinct a,b in S.
> Show that the number of elements of S <= 5.
> for example , {0,2,4} is such a set. I've coded a program to show that
> it's true for n <= 20000 where n is largest element of S, which is
> far from a proof though.

I'd divide a and b by gcd(a,b),
and then consider a prime factor of a-b.

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