Sur quelques équations indéterminées
Sur un problème de Fermat
Sur une équation diophantienne considérée par Goormaghtigh
Sur une question de V.A. Lebesgue
Nous démontrons une conjecture de V.A. Lebesgue relative à l’équation diophantienne par une méthode élémentaire qui fournit également la solution de quelques autres équations.
Systems of equations depending on certain ideals
The abc-inequality and the generalized Fermat equation in function fields
The arithmetic of Fermat curves.
The Diophantine equation f(x) = g(y)
The diophantine equation .
The diophantine equation .
The diophantine equation x² + C = yⁿ
The distribution of primes satisfying the condition
The equation
The equation
We show that the Diophantine equation of the title has, for , no solution in coprime nonzero integers and . Our proof relies upon Frey curves and related results on the modularity of Galois representations.
The Fermat equation with polynomial values as base variables.
The first case of Fermat's last theorem.
The lattice points of an n-dimensional tetrahedron.
The lattice points of an n-dimensional tetrahedron. (Summary).
The method of infinite ascent applied on
Each of the Diophantine equations has an infinite number of integral solutions for any positive integer . In this paper, we will show how the method of infinite ascent could be applied to generate these solutions. We will investigate the conditions when , and are pair-wise co-prime. As a side result of this investigation, we will show a method of generating an infinite number of co-prime integral solutions of the Diophantine equation for any co-prime integer pair .
The Mordell conjecture revisited