Title: Representing numbers as the sum of squares and powers in the ring $\mathbb{Z}_n$,
Abstract: We examine the representation of numbers as the sum of two squares in
$\mathbb{Z}_n$ for a general positive integer $n$. Using this information we
make some comments about the density of positive integers which can be
represented as the sum of two squares and powers of $2$ in $\mathbb{N}$.