Odd and Even: Difference of Squares (Posted on 2003-04-16)

Any product of two evens or two odds (sticking just to positives for the purpose of this problem) can be expressed as a difference of two perfect squares. 11*17=187=196-9 is an example.

A: Prove this idea.

B: Come up with a formula that gives the two perfect squares. Call the larger one a and the smaller one b.