Squares in arithmetic progression over cubic fields

Andrew Bremner, Samir Siksek

Research output: Contribution to journalArticlepeer-review


Euler showed that there can be no more than three integer squares in arithmetic progression. In quadratic number fields, Xarles has shown that there can be arithmetic progressions of five squares, but not of six. Here, we prove that there are no cubic number fields which contain five squares in arithmetic progression.

Original languageEnglish (US)
Pages (from-to)1409-1414
Number of pages6
JournalInternational Journal of Number Theory
Issue number5
StatePublished - Aug 1 2016


  • Arithmetic progressions
  • Jacobians
  • Mordell-Weil
  • cubic fields
  • curves
  • squares

ASJC Scopus subject areas

  • Algebra and Number Theory


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