On powers that are sums of consecutive like powers

Vandita Patel, Samir Siksek

Research output: Contribution to journalArticlepeer-review

Abstract

Let k≥ 2 be even, and let r be a non-zero integer. We show that for almost all d≥ 2 (in the sense of natural density), the equation xk+(x+r)k+⋯+(x+(d-1)r)k=yn,x,y,n∈Z,n≥2,has no solutions.

Original languageEnglish
Article number2
JournalResearch in Number Theory
Volume3
Issue number1
Early online date14 Feb 2017
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Bernoulli polynomial
  • Exponential equation
  • Newton polygon

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