Geodesic
Congruent numbers over real number fields
Tomasz Jędrzejak1
1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland
Colloquium Mathematicum, Tome 128 (2012) no. 2, pp. 179-186

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It is classical that a natural number $n$ is congruent iff the rank of $\mathbb{Q}$-points on $E_{n}:y^{2}=x^{3}-n^{2}x$ is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.
DOI : 10.4064/cm128-2-3
Keywords: classical natural number congruent rank mathbb points n positive paper following tada consider generalised congruent numbers extend above classical criterion several infinite families real number fields

Tomasz Jędrzejak 1

1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland 
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Tomasz Jędrzejak. Congruent numbers over real number fields. Colloquium Mathematicum, Tome 128 (2012) no. 2, pp. 179-186. doi: 10.4064/cm128-2-3

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