Squares in arithmetic progression over cubic fields

Andrew Bremner, Samir Siksek

Research output: Contribution to journalArticle

Abstract

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)
JournalInternational Journal of Number Theory
DOIs
StateAccepted/In press - 2015

ASJC Scopus subject areas

  • Algebra and Number Theory

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