# 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

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 30 REFERENCES