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

Karolina Krawciów (2011)

Colloquium Mathematicae

This paper focuses on the Diophantine equation x + p α y = M z ³ , with fixed α, p, and M. We prove that, under certain conditions on M, this equation has no non-trivial integer solutions if n ( M , p α ) , where ( 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].

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