Diophantine Equations and Bernoulli Polynomials View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2002-04

AUTHORS

Yu. F. Bilu, B. Brindza, P. Kirschenhofer, Á. Pintér, R. F. Tichy, A. Schinzel

ABSTRACT

Given m, n ≥ 2, we prove that, for sufficiently large y, the sum 1n +···+ yn is not a product of m consecutive integers. We also prove that for m ≠ n we have 1m +···+ xm ≠ 1n +···+ yn, provided x, y are sufficiently large. Among other auxiliary facts, we show that Bernoulli polynomials of odd index are indecomposable, and those of even index are ‘almost’ indecomposable, a result of independent interest. More... »

PAGES

173-188

References to SciGraph publications

  • 1987-12. Erratum to: On the diophantine equation 1k+2k+...+xk+R(x)=yz in ACTA MATHEMATICA
  • 1997. Some Methods of Erdôs Applied to Finite Arithmetic Progressions in THE MATHEMATICS OF PAUL ERDÖS I
  • 1973. Topics in Analytic Number Theory in NONE
  • 2000-06. Octahedrons with Equally Many Lattice Points in PERIODICA MATHEMATICA HUNGARICA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1014972217217

    DOI

    http://dx.doi.org/10.1023/a:1014972217217

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1006077877


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