Three cubes in arithmetic progression over quadratic fields

@article{GonzlezJimnez2010ThreeCI,
  title={Three cubes in arithmetic progression over quadratic fields},
  author={Enrique Gonz{\'a}lez-Jim{\'e}nez},
  journal={Archiv der Mathematik},
  year={2010},
  volume={95},
  pages={233-241}
}
  • Enrique González-Jiménez
  • Published 2010
  • Mathematics
  • Archiv der Mathematik
  • We study the problem of the existence of arithmetic progressions of three cubes over quadratic number fields $${{\mathbb{Q}(\sqrt{D})}}$$, where D is a squarefree integer. For this purpose, we give a characterization in terms of $${{\mathbb{Q}(\sqrt{D})}}$$-rational points on the elliptic curve E : y2 = x3 − 27. We compute the torsion subgroup of the Mordell–Weil group of this elliptic curve over $${{\mathbb{Q}(\sqrt{D})}}$$ and we give an explicit answer, in terms of D, to the finiteness of… CONTINUE READING

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