Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

Yıl 2021, , 51 - 55, 31.08.2021

Moussa Fall

https://doi.org/10.33187/jmsm.931258

Cited By: 1

Öz

In this paper, we give a parametrization of algebraic points of degree at most $4$ over $\mathbb{Q}$ on the schaeffer curve $\mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr. Mat 29:1151-1157, 2018) the set of algebraic points of degree at most $3$ over $\mathbb{Q}$ on this curve.

Anahtar Kelimeler

Degree of algebraic points, Plan curve, Rational points

Kaynakça

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• [5] M. Fall, O. Sall, Ponts alg´ebriques de petit degr´e sur la courbe d’´equation affine y2 = x5 +1, Afr. Mat. 29 (2018) 1151-1157.
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• [7] S. Siksek, M. Stoll, Partial descent on hyper elliptic curves and the generalized Fermat equation x3 +y4 +z5 = 0, Bulletin of the LMS 44 (2012) 151 -166