English

Sum of two repdigits a square

Number Theory 2018-01-22 v1

Abstract

A \emph{repdigit} is a natural number greater than 10 which has all of its base-10 digits the same. In this paper we find all examples of two repdigits adding to a square. The proofs lead to interesting questions about consecutive quadratic residues and non-residues, and provide an elementary application of elliptic curves.

Keywords

Cite

@article{arxiv.1607.06681,
  title  = {Sum of two repdigits a square},
  author = {Bart Goddard and Jeremy Rouse},
  journal= {arXiv preprint arXiv:1607.06681},
  year   = {2018}
}

Comments

9 pages

R2 v1 2026-06-22T15:01:40.803Z