On the Diophantine equation

Michael A. Bennett; Kálmán Győry; Ákos Pintér

doi:10.1112/S0010437X04000508

Abstract

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In this paper, we resolve a conjecture of Schäffer on the solvability of Diophantine equations of the shape $1^k + 2^k + \dotsb + x^k = y^n$, for $1 \leq k \leq 11$. Our method, which may, with a modicum of effort, be extended to higher values of k, combines a wide variety of techniques, classical and modern, in Diophantine analysis.

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Article contents

On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$

Abstract

Keywords

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