On the equation 1k + 2k + ... + xk = yn

K. Györy, Á Pintér

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In our paper a survey is given on the title equation. General finiteness theorems, bounds on n and the number of solutions, complete solution for small values of k, and some generalizations and analogues are presented. The basic ideas of the most important proofs are also outlined. We note that in the proofs of the recent results virtually every technique of modern Diophantine analysis has been employed.

Original languageEnglish
Pages (from-to)403-414
Number of pages12
JournalPublicationes Mathematicae
Volume62
Issue number3-4
Publication statusPublished - 2003

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Number of Solutions
Finiteness
Analogue
Theorem
Generalization

Keywords

  • Bernoulli polynomials
  • Superelliptic equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the equation 1k + 2k + ... + xk = yn . / Györy, K.; Pintér, Á.

In: Publicationes Mathematicae, Vol. 62, No. 3-4, 2003, p. 403-414.

Research output: Contribution to journalArticle

Györy, K & Pintér, Á 2003, 'On the equation 1k + 2k + ... + xk = yn ', Publicationes Mathematicae, vol. 62, no. 3-4, pp. 403-414.
Györy, K. ; Pintér, Á. / On the equation 1k + 2k + ... + xk = yn In: Publicationes Mathematicae. 2003 ; Vol. 62, No. 3-4. pp. 403-414.
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