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

Karolina Krawciów. "On generalized Fermat equations of signature (p,p,3)." Colloquium Mathematicae 123.1 (2011): 49-52. <http://eudml.org/doc/283919>.

@article{KarolinaKrawciów2011,
abstract = {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].},
author = {Karolina Krawciów},
journal = {Colloquium Mathematicae},
keywords = {Generalized Fermat equation; Elliptic curve associated to a solution; Galois representation on n-torsion points},
language = {eng},
number = {1},
pages = {49-52},
title = {On generalized Fermat equations of signature (p,p,3)},
url = {http://eudml.org/doc/283919},
volume = {123},
year = {2011},
}

TY - JOUR
AU - Karolina Krawciów
TI - On generalized Fermat equations of signature (p,p,3)
JO - Colloquium Mathematicae
PY - 2011
VL - 123
IS - 1
SP - 49
EP - 52
AB - 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].
LA - eng
KW - Generalized Fermat equation; Elliptic curve associated to a solution; Galois representation on n-torsion points
UR - http://eudml.org/doc/283919
ER -