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
I cannot provide any derivation of proof, but here is a formula, modified from the one provided by tomarken, that will provide for the pair (7,33) and many others:
if a is a prime number,
b = ((a-1)/2)2 + (a2-1)/2
Edited on April 25, 2006, 12:35 pm
Posted by Dej Mar
on 2006-04-25 12:26:43