11 citations · 18 across the 9 of their papers we have counts for
13 papers
Revisiting the Fermat-type equation
Nicolas Billerey, Imin Chen, Lassina Dembélé +2
We solve the Fermat-type equation \[ x^{13} + y^{13} = 3 z^7, \qquad \gcd(x,y,z) = 1 \] combining a unit sieve, the multi-Frey modular method, level raising, computations of system…
On Darmon's program for the Generalized Fermat equation, II
Nicolas Billerey, Imin Chen, Luis Dielefait +1
We obtain additional Diophantine applications of the methods surrounding Darmon's program for the generalized Fermat equation developed in the first part of this series of papers.…
On Darmon's program for the generalized Fermat equation, I
Nicolas Billerey, Imin Chen, Luis Dieulefait +1
In 2000, Darmon described a program to study the generalized Fermat equation using modularity of abelian varieties of -type over totally real fields. The original ap…
Some extensions of the modular method and Fermat equations of signature
Nicolas Billerey, Iimin Chen, Lassina Dembele +2
We provide several extensions of the modular method which were motivated by the problem of completing previous work to prove that, for any integer , the equation \[ x^{13…
A multi-Frey approach to Fermat equations of signature
Nicolas Billerey, Imin Chen, Luis Dieulefait +1
In this paper, we give a resolution of the generalized Fermat equations for all integers , and all integers $n…
On some remarkable congruences between two elliptic curves
Nicolas Billerey
We exhibit two non-isogenous rational elliptic curves with -torsion subgroups isomorphic as Galois modules.