```Date: Mar 20, 2013 5:36 PM
Author: James Waldby
Subject: Re: -----   ----- -- Solutions of an equation

On Wed, 20 Mar 2013 07:03:52 -0700, Deep wrote:> Consider (1) below under the given conditions:> > XY = AB       (1) > > Conditions: X, Y, A, B are odd integers each > 1.> The symbol (m, n)  = 1 means m, n are coprime odd integers each > 1. Example m = 3, n = 35.> (X, Y) = 1, (A, B) = 1> > Statement:: Given (1) one gets:> > X = A and Y = B              (2)  or> > X = a and Y = b              (3) where AB = ab,  (a, b) = 1> > Any valid comment upon the correctness of the Statement will be appreciated.Neither (2) nor (3) necessarily follows from (1) given (X,Y)=1 and (A,B)=1.  For example, let X = 3*5, Y = 7*11, A = 3*7, B = 5*11.Clearly (2) does not hold.  For (3), we have AB = 3*5*7*11 so can take a = 3*7, b = 5*11 and haveneither X=a nor Y=B, so (3) doesn't hold.However, if you rephrase (3) as "There exist a,b such that (a,b)=1, A*B = a*b, X=a, Y=b" then (3) follows trivially from (1) given (X,Y)=1 and (A,B)=1. -- jiw
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