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

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 Pubkeybreaker Posts: 1,683 Registered: 2/12/07
Re: ----------- relatively prime integers
Posted: Sep 18, 2011 7:25 AM

On Sep 17, 11:28 pm, William Elliot <ma...@rdrop.com> wrote:
> 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.

>
> ----

It is much simpler. Note that GCD(a,b) = GCD(a-b, b)........

Date Subject Author
9/17/11 Deep Deb
9/17/11 William Elliot
9/18/11 Pubkeybreaker