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
Partial Solution by tomarken)
As exemplified by (3,5), (6,10), (9,15),(12,20), any integral multiple of one solution is another solution, so each such family of a given ratio has infinitely many members.

Posted by Charlie
on 20060425 09:54:50 