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 = m^{2} - n^{2}. 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.*

No doubt.