Arithmetic progressions of Carmichael numbers in a reduced residue class

William D. Banks

Arithmetic progressions of Carmichael numbers in a reduced residue class

Number Theory 2020-10-14 v1

Authors: William D. Banks

Abstract

Fix coprime natural numbers $a,q$ . Assuming the Prime $k$ -tuple Conjecture, we show that there exist arbitrarily long arithmetic progressions of Carmichael numbers, each of which lies in the reduced residue class $a$ mod $q$ and is a product of three distinct prime numbers.

Keywords

prime numbers prime number theory arithmetic progressions

Cite

@article{arxiv.2010.06013,
  title  = {Arithmetic progressions of Carmichael numbers in a reduced residue class},
  author = {William D. Banks},
  journal= {arXiv preprint arXiv:2010.06013},
  year   = {2020}
}

Comments

5 pages

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