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Topic: ----------- relatively prime integers
Replies: 2   Last Post: Sep 18, 2011 7:25 AM

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William Elliot

Posts: 248
Registered: 10/7/08
Re: ----------- relatively prime integers
Posted: Sep 17, 2011 11:28 PM
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On Sat, 17 Sep 2011, Deep wrote:

> Let x and y be two integers each > 0 such that x and y
> are coprime and 2|y.

> Conjecture: (x + y ) , (x - y) ,y , x are coprime integers.

If prime p | x+y, x-y, then p | 2x, 2y.
If not p | 2, then p | x,y, so p = 2.
Consequently 2 | x+y, which's a no, no.

> It seems the conjecture is intuitavely correct. Any convincing
> argument will be appreciated.


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