Suppose a and b are positive integers. We all know that aČ+2ab+bČ is a perfect square. Give an example where also aČ+ab+bČ is a perfect square. How many such examples exist?
(In reply to
re(3): Partial Solution by Charlie)
Yeah, I noticed that there were some pairs you had come up with (like 7 and 33) that wouldn't be found by my formula. I'm not sure if there is an alternate way to find those other pairs, I didn't immediately recognize a pattern...
I'll see if I can come up with some kind of proof for why the formula I came up with works, although that's not really my area of expertise. :)

Posted by tomarken
on 20060425 11:08:12 