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.

I stink at and despise proofs, so I leave that to another puzzler.

But as for part B...(I think) it goes like this:
x = the smaller integer
y = the larger integer
a = the larger perfect square
b = the smaller perfect square

a = ((x+y)/2)^2
b = (y-((x+y)/2)^2

a-b=x*y

Posted by Hank on 2003-04-16 08:02:24