English

Squares in arithmetic progression over number fields

Algebraic Geometry 2009-09-10 v1 Number Theory

Abstract

We show that there exists an upper bound for the number of squares in arithmetic progression over a number field that depends only on the degree of the field. We show that this bound is 5 for quadratic fields, and also that the result generalizes to kk-powers for k>1k>1.

Keywords

Cite

@article{arxiv.0909.1642,
  title  = {Squares in arithmetic progression over number fields},
  author = {Xavier Xarles},
  journal= {arXiv preprint arXiv:0909.1642},
  year   = {2009}
}

Comments

17 pages

R2 v1 2026-06-21T13:44:16.492Z