English

The MHS algebra and supercongruences

Number Theory 2017-06-22 v3

Abstract

A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain generalizations of the harmonic numbers. We apply the technique to derive many new supercongruences. We also provide software for finding and proving supercongruences using our technique.

Keywords

Cite

@article{arxiv.1608.06864,
  title  = {The MHS algebra and supercongruences},
  author = {Julian Rosen},
  journal= {arXiv preprint arXiv:1608.06864},
  year   = {2017}
}

Comments

31 pages, comments are welcome. Part of v1 of this paper is now a separate submission: "The completed finite period map and Galois theory of supercongruences",arXiv:1703.04248

R2 v1 2026-06-22T15:29:28.835Z