On the Diophantine equation 1k + 2k + ⋯ + xk = yn

Michael A. Bennett, Kálmán Gyory, Ákos Pintér

Research output: Article

24 Citations (Scopus)

Abstract

In this paper, we resolve a conjecture of Schäffer on the solvability of Diophantine equations of the shape 1k + 2k + ⋯ + xk = yn, for 1 ≤ k ≤ 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.

Original languageEnglish
Pages (from-to)1417-1431
Number of pages15
JournalCompositio Mathematica
Volume140
Issue number6
DOIs
Publication statusPublished - dec. 1 2004

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'On the Diophantine equation 1<sup>k</sup> + 2<sup>k</sup> + ⋯ + x<sup>k</sup> = y<sup>n</sup>'. Together they form a unique fingerprint.

  • Cite this