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: Partial Solution
As Charlie pointed out, the solutions can go on infinitely as long as they are integral multiples of one of the "base pairs". Here is the formula to find the base pairs, which themselves appear to go on infinitely:
Let a = any prime number greater than or equal to 5.
b = ((a-1)/2)^2 - 1
As long as you choose a prime number for a, you can find the value for b that will make a^2 + ab + b^2 = a perfect square.
Posted by tomarken
on 2006-04-25 10:08:34