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)
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 = ((a1)/2)^{2} + (a^{2}1)/2
Edited on April 25, 2006, 12:35 pm

Posted by Dej Mar
on 20060425 12:26:43 