Squares in arithmetic progression over cubic fields
classification
🧮 math.NT
keywords
arithmeticsquaresfieldsprogressiontherecubicfivenumber
read the original 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.
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