Newsgroups: rec.puzzles
From: Dan Hoey <haoyuep@aol.com>
Date: Tue, 15 Dec 2009 15:00:33 -0500
Subject: Re: Integer right triangles

Mark Brader wrote:
> Rich Grise:
>> Well, that got me to thinking - everybody knows about the 3,4,5 and the
>> 5,12,13 right triangles; I'm wondering if, other than their multiples
>> (6,8,10; 10,24,26 etc.) are there any other integer right triangles?

> Yes.

>> If so, is(are?) there an infinite number of them?

> Yes.  See e.g. http://mathworld.wolfram.com/PythagoreanTriple.html

That page has a lot of stuff, making it easy to miss equation 11:

If  u > v  are positive integers, relatively prime and not both
odd, then the numbers

  2uv, u^2-v^2, u^2+v^2

form a Pythagorean triple, and every Pythagorean triple is generated
by exactly one such pair (u,v).

Dan