A congruence for some generalized harmonic type sums

Goral H., Sertbas D. C.

INTERNATIONAL JOURNAL OF NUMBER THEORY, cilt.14, sa.4, ss.1033-1046, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1142/s1793042118500628
  • Dergi Adı: INTERNATIONAL JOURNAL OF NUMBER THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1033-1046
  • Anahtar Kelimeler: Hyperharmonic numbers, Wolstenholme's type congruences, SPECIAL VALUES, ZETA-FUNCTION, NUMBERS
  • Çukurova Üniversitesi Adresli: Hayır

Özet

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.