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Re:  question about coprimality
Posted:
Sep 17, 2011 7:30 AM


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 2b 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)(cb) = 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),(cb) are coprime. Then it follows c+b = d and c  b = e where d, e are coprime and both are odd. d and e need not be unique. But (2.1) and (2.2) are valid but not unique. You may like to comment.    



