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?

Here are some examples of pairs of values (a and b are interchangeable, of course):

 a     b
---------
 3    5
 7    8
 6    10
 9    15
 5    16 
 14  16
 12  20

I'm not sure at this point how many more examples exist...

Posted by tomarken on 2006-04-25 09:38:18