Fascinating Fact about Pythagorean Triplets

Everybody knows what a Pythagorean triplet is, it is the tuple (a,b,c) such that a² + b² = c². It turns out that if we restrict ourselves to the set of primitive integral pythagorean triplets, every such triplet where a, b and c are coprime can be represented by integers m, n where

a = m² - n²
b = 2mn
c = m² + n²

Besides being of mathematical interest, this result also gives us an efficient method to enumerate integral pythagorean triplets.

Visit this link for the proof.

UPDATE: The link seems to imply that the relation holds for all a,b,c. But I think there is a flaw in the proof when the author assumes that since a² is square, c-b and c+b must also be square. It seems to me that this is not necessarily true unless c-b and c+b are coprime. This is why I added the qualification that a, b and c must be coprime.

All feedback is welcome. :-)