"The fact is that for m and n coprime of different parities, (*) yields coprime numbers a, b, and c. Conversely, all coprime triples can indeed be obtained in this manner. All others are multiples of coprime triples: ka, kb, kc."

I was playing around and found the triple (21, 72, 75). 2nm is 72 so nm is 36, the only coprime divisiors are 1 and 36. The triple associated with the pair (1,36) is m^2-n^2, 2nm, n^2+m^2: 1295, 72, 1297. This is not (21,72,75).

So how is it that all coprime triples are of this form? Did I miss something?

Steve

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