English

Factorials and Legendre's three-square theorem

Number Theory 2021-01-06 v1

Abstract

We provide a necessary and sufficient condition for n!n! to be a sum of three squares. The condition is based on the binary representation of nn and can be expressed by the operation of an automaton.

Keywords

Cite

@article{arxiv.2101.01567,
  title  = {Factorials and Legendre's three-square theorem},
  author = {Rob Burns},
  journal= {arXiv preprint arXiv:2101.01567},
  year   = {2021}
}

Comments

8 pages, 1 table, 1 figure

R2 v1 2026-06-23T21:48:00.454Z