Putnam 1974 A3

A well-known theorem asserts that a prime $p > 2$ can be written as the sum of two perfect squares ( $p = m^2 +n^2$ , with $m$ and $n$ integers) if and only if $p \equiv 1$ (mod $4$ ). Assuming this result, find which primes $p > 2$ can be written in each of the following forms, using integers $x$ and $y$ : a) $x^2 +16y^2,$ b) $4x^2 +4xy+ 5y^2.$