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Topic: ------------- question about coprimality
Replies: 2   Last Post: Sep 17, 2011 7:30 AM

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Deep Deb

Posts: 420
Registered: 12/6/04
------------- question about coprimality
Posted: Sep 16, 2011 8:42 PM
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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.

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