Representing numbers as the sum of squares and powers in the ring $\mathbb{Z}_n$

Rob Burns

Representing numbers as the sum of squares and powers in the ring $\mathbb{Z}_n$

Number Theory 2017-09-26 v2

Authors: Rob Burns

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 $\mathbb{N}$ .

Keywords

sum of squares ring $\mathbb{Z}_n$ number representation number theory integer density

Cite

@article{arxiv.1708.03930,
  title  = {Representing numbers as the sum of squares and powers in the ring $\mathbb{Z}_n$},
  author = {Rob Burns},
  journal= {arXiv preprint arXiv:1708.03930},
  year   = {2017}
}

Comments

11 pages

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