Prove that every prime number other than 2, can be expressed as a difference of two squares.

- Princeton Math Club Website

Hello,

Sorry for bumping an old one, but isnt this true for any odd number in general, not necesarily an odd prime.

2^2 - 1^2 = 3

3^2 - 2^2 = 5

4^2 - 3^2 = 7

5^2 - 4^2 = 9

The difference between squares of any two consecutive numbers x+1 and x can be given by 2x+1. This will include 9,15,21 etc as well.

Posted by Vishal Gupta on 2010-09-14 15:19:10