Families of curves having each an integer point
Familles d'équations de Thue-Mahler n'ayant que des solutions triviales
Fuchssche Gruppen, die freies Produkt zweier zyklischer Gruppen sind, und die Gleichung x2 + y2 + z2 = xyz.
Gaussiana
Generators and integer points on the elliptic curve y² = x³ - nx
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...
Homoroot integer numbers.
In Gaussian integers has only trivial solutions – a new approach.
Integer Points and the Rank of Thue Elliptic Curves.
Integer points on curves of genus 1
Integral Points on Certain Elliptic Curves
Integral points on elliptic curves defined by simplest cubic fields.
Integral points on the elliptic curve
Let be a fixed odd prime. We combine some properties of quadratic and quartic Diophantine equations with elementary number theory methods to determine all integral points on the elliptic curve . Further, let denote the number of pairs of integral points on with . We prove that if , then or depending on whether or .
Jednoduché nové řešení diofantické rovnice
Laurent polynomials and superintegrable maps.
Les équations diophantiennes , d’après Cassels
Les points exceptionnels rationnels sur certaine cubique du premier genre
L'étude des formes cubiques rationnelles via la méthode du cercle
Linear Spaces on the Intersection of Cubic Hypersurfaces.
Ljunggren's Diophantine problem connected with virus structure.
Lösbare Gleichungen axn - byn = c und Grundeinheiten für einige algebraische Zahlkörper vom Grade n = 3, 4, 6.