Nicolas Billerey

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math.NT2025

Revisiting the Fermat-type equation $x^{13} + y^{13} = 3 z^{7}$

Nicolas Billerey, Imin Chen, Lassina DembÃ©lÃ© +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…

math.NT2025

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 $GL_{2}$ -type over totally real fields. The original ap…

math.NT2024

A multi-Frey approach to Fermat equations of signature $(r, r, p)$

Nicolas Billerey, Imin Chen, Luis Dieulefait +1

In this paper, we give a resolution of the generalized Fermat equations $x^{5} + y^{5} = 3 z^{n} and x^{13} + y^{13} = 3 z^{n},$ for all integers $n \geq 2$ , and all integers $n…

Revisiting the Fermat-type equation x13+y13=3z7

On Darmon's program for the generalized Fermat equation, I

A multi-Frey approach to Fermat equations of signature (r,r,p)

Revisiting the Fermat-type equation $x^{13} + y^{13} = 3 z^{7}$

A multi-Frey approach to Fermat equations of signature $(r, r, p)$