Re^2: pythagorean triples

That's correct, but any integer multiple of a primitive Pythagorean triple is also a Pythagorean triple. (The proof is left as an exercise for the reader) This sequence generates the set of primitive Pythagorean triples (assuming that $m & $n are coprime)

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Comment on Re^2: pythagorean triples

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Re^3: pythagorean triples by chas (Priest) on Apr 24, 2006 at 04:36 UTC
Well, it's true that the primitive triples are of that form, but not conversely; 6,8,10 occurs for n=3,m=1 (which are coprime), and that triple isn't primitive. So the code generates primitive (i.e. having no common factor) triples, but some others as well. The real point is that it isn't so easy to print a list of all Pythagorean triples without duplication, and I guess that thought was what motivated my reply.	[reply]

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Re^3: pythagorean triples
by chas (Priest) on Apr 24, 2006 at 04:36 UTC

Well, it's true that the primitive triples are of that form, but not conversely; 6,8,10 occurs for n=3,m=1 (which are coprime), and that triple isn't primitive. So the code generates primitive (i.e. having no common factor) triples, but some others as well. The real point is that it isn't so easy to print a list of all Pythagorean triples without duplication, and I guess that thought was what motivated my reply.

[reply]