6 citations · 19 across the 11 of their papers we have counts for
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On the generalized Fermat equation
Alex J. Best, Sander R. Dahmen, Nuno Freitas
Let . We study the generalized Fermat equation \[x^{13}+y^{13}=z^n, \quad x,y,z \in \mathbb{Z}, \quad \gcd(x,y,z)=1.\] Using a combination of techniques,…
Explicitly bounding perfect powers in elliptic divisibility sequences
Sander R. Dahmen, Joey M. van Langen
In this paper we consider elliptic divisibility sequences generated by a point on an elliptic curve over with -invariant given by an integral short Weierstra…
Perfect powers expressible as sums of two fifth or seventh powers
Sander R. Dahmen, Samir Siksek
We show that the generalized Fermat equations with signatures (5,5,7), (5,5,19), and (7,7,5) (and unit coefficients) have no non-trivial primitive integer solutions. Assuming GRH,…
Level lowering modulo prime powers and twisted Fermat equations
Sander R. Dahmen, Soroosh Yazdani
We discuss a clean level lowering theorem modulo prime powers for weight cusp forms. Furthermore, we illustrate how this can be used to completely solve certain twisted Fermat…
A refined modular approach to the Diophantine equation
Sander R. Dahmen
Let be a positive integer and consider the Diophantine equation of generalized Fermat type in nonzero coprime integer unknowns . Using methods of modula…
On the residue class distribution of the number of prime divisors of an integer
Michael Coons, Sander R. Dahmen
The {\em Liouville function} is defined by $\gl(n):=(-1)^{Ω(n)}$ where is the number of prime divisors of counting multiplicity. Let $\z_m:=e^{2πi/m}$ be a primitive …