NO-ABEL 2015

The five sides of a regular pentagon are extended to lines $\ell_1, \ell_2, \ell_3, \ell_4$ , and $\ell_5$ . Denote by $d_i$ the distance from a point $P$ to $\ell_i$ . For which point(s) in the interior of the pentagon is the product $d_1d_2d_3d_4d_5$ maximal?

a. Determine all nonnegative integers $x$ and $y$ so that $3^x + 7^y$ is a perfect square and $y$ is even. b. Determine all nonnegative integers $x$ and $y$ so that $3^x + 7^y$ is a perfect square and $y$ is odd