On Carmichael numbers of the form $2^np^m+1$

Florian Luca

On Carmichael numbers of the form $2^np^m+1$

Number Theory 2026-06-27 v1

Authors: Florian Luca

Abstract

Here, we show that if $m\ge 5$ is fixed and odd, then there are only finitely many Carmichael numbers of the form $2^np^m+1$ for positive integers $n$ and prime $p$ .

Keywords

Carmichael numbers number theory exponential Diophantine form finiteness result

Cite

@article{arxiv.2606.28829,
  title  = {On Carmichael numbers of the form $2^np^m+1$},
  author = {Florian Luca},
  journal= {arXiv preprint arXiv:2606.28829},
  year   = {2026}
}