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Right triangles with algebraic sides and elliptic curves over number fields

In: Mathematica Slovaca, vol. 59, no. 3
Ernesto Girondo - G. González-Diez - E. González-Jiménez - R. Steuding - Jörn Steuding

Details:

Year, pages: 2009, 299 - 306
Keywords:
congruent number problem, number fields, elliptic curves
About article:
Given any positive integer $n$, we prove the existence of infinitely many right triangles with area $n$ and side lengths in certain number fields. This generalizes the famous congruent number problem. The proof allows the explicit construction of these triangles; for this purpose we find for any positive integer $n$ an explicit cubic number field $\Bbb Q(λ)$ (depending on $n$) and an explicit point $Pλ$ of infinite order in the Mordell-Weil group of the elliptic curve $Y2=X3-n2X$ over $\Bbb Q(λ)$.
How to cite:
ISO 690:
Girondo, E., González-Diez, G., González-Jiménez, E., Steuding, R., Steuding, J. 2009. Right triangles with algebraic sides and elliptic curves over number fields. In Mathematica Slovaca, vol. 59, no.3, pp. 299-306. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0126-3

APA:
Girondo, E., González-Diez, G., González-Jiménez, E., Steuding, R., Steuding, J. (2009). Right triangles with algebraic sides and elliptic curves over number fields. Mathematica Slovaca, 59(3), 299-306. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0126-3
About edition: