On congruences involving harmonic numbers H3n and H3n+r

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Elkhiri L., KOPARAL S., ÖMÜR N.

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

• 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
• Kocaeli 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}.