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Re^2: pythagorean triples

by thor (Priest)
on Apr 24, 2006 at 03:50 UTC ( #545192=note: print w/ replies, xml ) Need Help??


in reply to Re: pythagorean triples
in thread 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)

thor

The only easy day was yesterday


Comment on Re^2: pythagorean triples
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.

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