English

There are infinitely many elliptic Carmichael numbers

Number Theory 2018-08-01 v1

Abstract

In 1987, Dan Gordon defined an elliptic curve analogue to Carmichael numbers known as elliptic Carmichael numbers. In this paper, we prove that there are infinitely many elliptic Carmichael numbers. In doing so, we resolve in the affirmative the question of whether there exist infinitely square-free, composite integers nn such that for every prime pp that divides nn, p+1n+1p+1|n+1.

Keywords

Cite

@article{arxiv.1609.00231,
  title  = {There are infinitely many elliptic Carmichael numbers},
  author = {Thomas Wright},
  journal= {arXiv preprint arXiv:1609.00231},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1212.5850

R2 v1 2026-06-22T15:37:39.450Z