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 How many perfect squares (Posted on 2006-04-25)
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?

 See The Solution Submitted by Salil Rating: 3.0000 (2 votes)

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 re(2): Adding to the solution...even numbers! | Comment 13 of 19 |

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

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