English

Quartic Integral Polynomial Pell Equations

Number Theory 2023-07-11 v1

Abstract

In this paper we classify all monic, quartic, polynomials d(x)Z[x]d(x)\in\mathbb{Z}[x] for which the Pell equation f(x)2d(x)g(x)2=1f(x)^2-d(x)g(x)^2=1 has a non-trivial solution with f(x),g(x)Z[x]f(x),g(x)\in\mathbb{Z}[x].

Keywords

Cite

@article{arxiv.2307.04566,
  title  = {Quartic Integral Polynomial Pell Equations},
  author = {Zachary Scherr and Katherine Thompson},
  journal= {arXiv preprint arXiv:2307.04566},
  year   = {2023}
}
R2 v1 2026-06-28T11:25:58.895Z