Newsgroups: rec.puzzles
From: hoey@AIC.NRL.Navy.Mil (Dan Hoey)
Date: 20 May 92 11:43:25 GMT
Subject: Re: Extension to Perfect Squares

> I was fascinated with triplets (not the technical name I assure
> you), that had the property:
> x^2 + y^2 = z^2

They are called Pythagorean triples.

> After a lot of work (oh, to have known more than geometry) I came up
> with a simple formula to generate endless amounts of these triplets.

When I was in high school I found the ones of the form

  (2n+1)^2 + (2n(n+1))^2 = (2n(n+1) + 1)^2

but as I learned later, these are only the skinniest ones.

> However, finding the algorithm for squares should prove no problem here.

Find it in any introduction to number theory. It's in the rubber
bible, too, but I don't think they tell you why.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil