On congruences involving harmonic numbers H3n and H3n+r

Elkhiri L., KOPARAL S., ÖMÜR N.

Indian Journal of Pure and Applied Mathematics, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s13226-025-00848-9
  • Dergi Adı: Indian Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Anahtar Kelimeler: Abel sum, Congruences, Harmonic numbers
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this paper, we establish various congruences involving harmonic numbers H3n and H3n+r modulo prime number p, ie., ∑0≤k≤[p/3]H3k2(modp) and ∑0≤k≤[p/3]H3k+r3k+r(modp). Also, we give the generalization of Meštrović’s congruence, ie., for any prime number p≥5, (Formula presented.) where r∈{1,2,3}.