Squares in arithmetic progression over number fields

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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 k-powers for integers k> 1. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)379-389
JournalJournal of Number Theory
Issue number3
Publication statusPublished - 1 Mar 2012


  • Arithmetic progression
  • Gonality
  • Uniform bounds


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