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Let E be an elliptic curve over the rationals ℚ given by y² = x³ - nx with a positive integer n. We consider first the case where n = N² for a square-free integer N. Then we show that if the Mordell-Weil group E(ℚ ) has rank one, there exist at most 17 integer points on E. Moreover, we show that for some parameterized N a certain point P can be in a system of generators for E(ℚ ), and we determine the integer points in the group generated by the point P and the torsion points. Secondly, we consider...

Generators and integral points on twists of the Fermat cubic

Yasutsugu Fujita, Tadahisa Nara (2015)

Acta Arithmetica

We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell-Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.

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Gaussiana

Généralisation de la théorie des fractions continues

Generalization of a problem of Diophantus

Generalizations of Furtwängler's criteria for Fermat's last theorem and some related results.

Generalized ABC theorems for non-Archimedean entire functions of several variables in arbitrary characteristic

Generalized Frobenius numbers: bounds and average behavior

Generalized Lagrange criteria for certain quadratic Diophantine equations.

Generalized Vandermonde determinants

Generators and integer points on the elliptic curve y² = x³ - nx

Generators and integral points on twists of the Fermat cubic

Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables

Groupes de Picard et problèmes de Skolem. I

Groupes de Picard et problèmes de Skolem. II

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