## Integers (x,y) such that x – y and x*y are squares

There are pairs of numbers whose difference and product are perfect squares:

$x \; - \; y \; = \; a^2$
$x \, y \; = \; b^2$

Here are few examples where the smaller number of such a pair   y = 2, 3, 5, 7, 11, 13

$18 - 2 = 4^2$                         $18\times 2 = 6^2$
$12 - 3 = 3^2$                          $12\times 3 = 6^2$
$405 - 5 - 20^2$                      $405\times 5 = 45^2$
$448 - 7 = 21^2$                      $448\times 7 = 56^2$
$1100 - 11 = 33^2$                    $1100\times 11 = 110^2$
$5475613 - 13 = 2340^2$        $5475613\times 13 = 8437^2$