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(4): Partial Solution by Charlie)

Thanks for the list, Charlie!

It now seems that for all the prime numbers, a second value of b can be found:

b = a^2 - ((a+1)/2)^2

 

Posted by tomarken on 2006-04-25 11:40:02