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

  1. m = 1 (mod 3), n = 1 (mod 3), or
  2. m = 1 (mod 3), n = 2 (mod 3), or
  3. m = 2 (mod 3), n = 1 (mod 3), or
  4. 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.

No doubt.

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