Geodesic
On generalized Fermat equations of signature $(p,p,3)$
Karolina Krawciów1
1 Institute of Mathematics University of Szczecin 70-451 Szczecin, Poland
Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 49-52

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

This paper focuses on the Diophantine equation $x^n+p^{\alpha}y^n=Mz^3$, with fixed $\alpha$, $p$, and $M$. We prove that, under certain conditions on $M$, this equation has no non-trivial integer solutions if $n\geq \mathcal F(M,p^\alpha)$, where $\mathcal F(M,p^{\alpha})$ is an effective constant. This generalizes Theorem 1.4 of the paper by Bennett, Vatsal and Yazdani [Compos. Math. 140 (2004), 1399–1416].
DOI : 10.4064/cm123-1-4
Keywords: paper focuses diophantine equation alpha fixed alpha prove under certain conditions equation has non trivial integer solutions geq mathcal alpha where mathcal alpha effective constant generalizes theorem paper bennett vatsal yazdani compos math

Karolina Krawciów 1

1 Institute of Mathematics University of Szczecin 70-451 Szczecin, Poland 
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Karolina Krawciów. On generalized Fermat equations of signature $(p,p,3)$. Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 49-52. doi: 10.4064/cm123-1-4

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