Date: Sep 16, 2011 8:42 PM
Author: Deep Deb
Subject: ------------- question about coprimality

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 ?

Any helpful comment will be appreciated.