Subject: Re: Properties of Pythagorean Triples
Date: Wed, 07 Jul 2000 21:16:09 -0400
From: Alex Bogomolny
>I wrote my whole question on your CTK website (I think).
What question was it?
>Why, in a
>list of PPTs, is either a or b always a multiple of 3?
Say, a = 2mn, b = m2 - n2. If either m or n is a multiple of 3, so is a. Otherwise, either
- m = 1 (mod 3), n = 1 (mod 3), or
- m = 1 (mod 3), n = 2 (mod 3), or
- m = 2 (mod 3), n = 1 (mod 3), or
- m = 2 (mod 3), n = 2 (mod 3)
In either case b = 0 (mod 3). Can you handle the rest from here?
>Your help will be appreciated.