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On the congruent number problem over integers of cyclic number fields

In: Mathematica Slovaca, vol. 66, no. 3
Albertas Zinevičius
Detaily:
Rok, strany: 2016, 561 - 564
Kľúčové slová:
congruent numbers, cyclic extensions, rings of integers, prime numbers
O článku:
Given a cyclic field extension $K/\mathbb{Q}$ of degree $d$ and a nonzero rational integer $m$, we show that the equation $mp^2 = x^4 - y^2$ has no nontrivial solutions in \mathcal{O}_K$ when $p$ belongs to a subset of rational prime numbers of relative density at least $\varphi(d)/(2d)$.
Ako citovať:
ISO 690:
Zinevičius, A. 2016. On the congruent number problem over integers of cyclic number fields. In Mathematica Slovaca, vol. 66, no.3, pp. 561-564. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0158

APA:
Zinevičius, A. (2016). On the congruent number problem over integers of cyclic number fields. Mathematica Slovaca, 66(3), 561-564. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0158
O vydaní:
Publikované: 1. 6. 2016