```Date: Sep 17, 2011 7:30 AM
Author: Deep Deb
Subject: Re: ------------- question about coprimality

On Sep 17, 4:36 am, quasi <qu...@null.set> wrote:> On Fri, 16 Sep 2011 17:42:31 -0700 (PDT), Deep <deepk...@yahoo.com>> wrote:>> >Let a, b, c be three coprime integers such that 2|b and none> >is a prime. Further let a = de where d and e are coprime. Now> >consider (1)>> >c^2 - b^2 = a^2               (1).  >> >From (1) one gets (2) and then (2.1) and (2.2)>> >(c + b )(c - b) = (de)^2     (2);    >> >c + b = d^2       (2.1)> >c - b = e^2       (2.2)>> >Question: Are (2.1) and (2.2) unique ? If not why not ?>> No -- there are lots of counterexamples.>> For example, if a=33 the equation>>    (c+b)(c-b) = a^2>> has more than one solution satisfying your conditions:>>    c=65, b=56 (which corresponds to d=3, e=11)>>    c=545, b=544 (which corresponds to d=1, e=33)>> quasi-----  -----   ------You are right. My question is if (c+b),(c-b) are coprime. Then itfollowsc+b = d and c - b = e where d, e are coprime and both are odd. d and eneed not be unique.But (2.1) and (2.2) are valid but not unique.You may like to comment.----  ----  ----   -----
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