What does this research mean for the field?

Certain congruences involving generalized Catalan numbers and harmonic numbers hold true modulo p(2). Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to establish specific congruences related to generalized Catalan and harmonic numbers under modulo p(2).

March 1, 2026

On Congruences Involving the Generalized Catalan Numbers and Harmonic Numbers

Key Points

The aim is to establish specific congruences related to generalized Catalan and harmonic numbers under modulo p(2).
Developed mathematical proofs for congruences
Analyzed relationships between generalized Catalan and harmonic numbers
Applied modular arithmetic techniques
Established new congruences for generalized Catalan numbers
Identified patterns in harmonic numbers under modulo p(2)
Provided insights into number theory and divisibility properties

Abstract

In this paper, we prove some congruences involving the generalized Catalan numbers and harmonic numbers modulo p(2), one of which is

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On Congruences Involving the Generalized Catalan Numbers and Harmonic Numbers

Key Points

Abstract

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