A family of quintic Thue equations via Skolem's $p$-adic method

Davide Lombardo

A family of quintic Thue equations via Skolem's $p$-adic method

Number Theory 2022-08-09 v1

Authors: Davide Lombardo

Abstract

In this semi-expository article we solve the diophantine equation $m^5+(4 \cdot 5^4 b^4)mn^4 - n^5=1$ for all integers $b \neq 0$ . This gives an example of a family of quintic Thue equations that can be solved completely by using nothing more than Skolem's $p$ -adic method. We also give a general introduction to Skolem's method from a modern perspective.

Keywords

quintic thue equations skolem p-adic method diophantine equation power-law family expository article

Cite

@article{arxiv.2208.03830,
  title  = {A family of quintic Thue equations via Skolem's $p$-adic method},
  author = {Davide Lombardo},
  journal= {arXiv preprint arXiv:2208.03830},
  year   = {2022}
}

Comments

Dedicated to Roberto Dvornicich on the occasion of his 70th birthday, 10 pages

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