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.

The solution is:

(sqrt a + sqrt b) * (sqrt a - sqrt b)= x = a - b

Where:
a is the largest of the squares,
b is the smallest of the squares, and
x is the product/difference

Posted by jennifer on 2003-04-16 08:07:59