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.

(In reply to re(2): solution by Charlie)

In my solution, I used the integers and not the perfect squares... Just substitute sqrt(a) for a and sqrt(b) for b if you want to get the perfect squares and not the roots.

This is especially useful for easy multiplication. If asked what 23^2 was, you could just figure out what 20*26+(3^2) which is just 520+9 = 529

Posted by Gamer on 2003-04-16 11:15:51