I recently investigated which numbers can be represented at the sum of one square number and double a different square number, for instance 9 is 1+2(4), or 38 is 36+2(1).

With pencil and paper: 99 is the smallest number that can be represented as a^2 + 2b^2 in three different ways: find them all!

With a computer: what is the smallest number that can be represented as a^2 + 2b^2 (with a and b different positive integers) in six different ways?