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

- Princeton Math Club Website

Any given prime number other than 2 (m, say)must be odd.

Thus, we can substitute m = 2x+1.

Since, m>=3, it follows that x>=1.

Now,

m = 2x+1

= (x+1)^2 - x^2, where x>=1

Consequently, any given prime number other than 2 ia always expressible as the difference of two squares.

*Edited on ***January 23, 2008, 10:37 am**