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(2): Partial Solution by tomarken)
The formula does seem to work. I haven't worked out how it works however; I'd like to see the derivation or proof.
The formula does not, however, provide all the base pairs. While it provides (7,8), it does not provide (7,33). It doesn't provide those base pairs where neither member is prime, such as (16,39) or (65,88).
But it does show there are infinitely many base pairs.

Posted by Charlie
on 20060425 11:03:53 