Given that, a, b, and c are all positive integers so that a < b < c, and 1/a, 1/b, and 1/c are in arithmetic progression, can a² + b² be equal to c²?
(In reply to re: I think I have it
"Maybe you meant to set 1/b + k = 1/c and 1/a +2k = 1/c."
That's right Eric, that's exactly what I did - I just posted it wrong. I fixed my post. Thanks for catching this.
"Also, I don't think k has to be an integer, it just has to be rational."
I suppose there might be other definitions of "arithmetic progression" out there, but the one I'm looking at shows that k must be an integer (CRC Concise Encyclopedia of Mathematics, Eric W. Weisstein, 1999).
Posted by Mindrod
on 2006-02-08 09:30:19