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 $\mathbb{N}$.

11 pages