A congruence for some generalized harmonic type sums

Goral H., Sertbas D. C.

INTERNATIONAL JOURNAL OF NUMBER THEORY, vol.14, no.4, pp.1033-1046, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1142/s1793042118500628
  • Journal Name: INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1033-1046
  • Keywords: Hyperharmonic numbers, Wolstenholme's type congruences, SPECIAL VALUES, ZETA-FUNCTION, NUMBERS
  • Çukurova University Affiliated: No

Abstract

In 1862, Wolstenholme proved that the numerator of the (p - 1)th harmonic number is divisible by p(2) for any prime p >= 5. A variation of this theorem was shown by Alkan and Leudesdorf. Motivated by these results, we prove a congruence modulo some odd primes for some generalized harmonic type sums.