English

On Amicable Numbers

History and Overview 2025-09-08 v2 Number Theory

Abstract

This is an English translation of Euler's 1750 paper "De numeris amicabilibus" (E152), the most substantial of his three works with this name. In it, he expounds at great length the ad hoc methods he has developed to search for pairs of amicable numbers, concluding with a list of around 60 new pairs.

Keywords

Cite

@article{arxiv.2409.08783,
  title  = {On Amicable Numbers},
  author = {Leonhard Euler and Jonathan David Evans},
  journal= {arXiv preprint arXiv:2409.08783},
  year   = {2025}
}

Comments

79 pages, including two appendices. Updated following referees' comments. Accepted for publication in Euleriana