On generalized Fermat equations of signature (p,p,3)

• Autorzy: Karolina Krawciów
• Języki publikacji: EN

Abstrakty

EN

This paper focuses on the Diophantine equation $xⁿ+p^{α}yⁿ = Mz³$, with fixed α, p, and M. We prove that, under certain conditions on M, this equation has no non-trivial integer solutions if $n ≥ ℱ(M,p^{α})$, where $ℱ(M,p^{α})$ is an effective constant. This generalizes Theorem 1.4 of the paper by Bennett, Vatsal and Yazdani [Compos. Math. 140 (2004), 1399-1416].

Kategorie tematyczne

• 11D41: Higher degree equations; Fermat's equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 123
• Numer: 1
• Strony: 49-52

Daty

wydano

2011

Twórcy

autor

Karolina Krawciów

• Institute of Mathematics, University of Szczecin, 70-451 Szczecin, Poland

Identyfikatory

DOI

10.4064/cm123-1-4