Generalized Mersenne Numbers of the form $cx^2$

Azizul Hoque

Generalized Mersenne Numbers of the form $cx^2$

Number Theory 2022-05-13 v1

Authors: Azizul Hoque

Abstract

Generalized Mersenne numbers are defined as $M_{p,n} = p^n - p + 1$ , where $p$ is any prime and $n$ is any positive integer. Here, we prove that for each pair $(c, p)$ with $c\geq 1$ an integer, there is at most one $M_{p, n}$ of the form $cx^2$ with a few exceptions.

Keywords

number theory

Cite

@article{arxiv.2205.06235,
  title  = {Generalized Mersenne Numbers of the form $cx^2$},
  author = {Azizul Hoque},
  journal= {arXiv preprint arXiv:2205.06235},
  year   = {2022}
}

Comments

5 pages; to appear in `Annales Mathematicae et Informaticae'

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