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 language | English (US) |
|---|---|
| Pages (from-to) | 1409-1414 |
| Number of pages | 6 |
| Journal | International Journal of Number Theory |
| Volume | 12 |
| Issue number | 5 |
| DOIs | |
| State | Published - Aug 1 2016 |
Keywords
- Arithmetic progressions
- Jacobians
- Mordell-Weil
- cubic fields
- curves
- squares
ASJC Scopus subject areas
- Algebra and Number Theory
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