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: Adding to the solution...even numbers!
Turns out that that last formula works for any multiple of 4, not just multiples of 8, but if "a" is not divisible by 8 it just produces an integer multiple of one of the odd-numbered solutions.
Here is another formula that works - again, it will produce solutions for any value of "a" that is a multiple of 4, but only those multiples of 8 will produce unique "base pairs":
b = (a^2 - 8a - 48)/16
Posted by tomarken
on 2006-04-26 12:58:02