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 question about coprimality
Posted:
Sep 16, 2011 8:42 PM


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 ?
Any helpful comment will be appreciated.



