What does this research mean for the field?

New congruences with the generalized Catalan numbers and harmonic numbers modulo p(2) are established for prime numbers p greater than 3. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to discover new relationships between generalized Catalan numbers and harmonic numbers under modulo operations.

March 1, 2026

New Congruences With the Generalized Catalan Numbers and Harmonic Numbers

Key Points

The aim is to discover new relationships between generalized Catalan numbers and harmonic numbers under modulo operations.
Analysis of congruences relating to generalized Catalan numbers
Exploration of properties of harmonic numbers
Examination of results under modulo p for prime numbers greater than 3
Established novel congruences involving generalized Catalan numbers and harmonic numbers
Demonstrated specific properties under modulo p, increasing understanding of number theory
Provided evidence for deeper connections between these mathematical entities

Abstract

In this paper, we give new congruences with the generalized Catalan numbers and harmonic numbers modulo p(2). One of our results is as follows: for prime number p > 3,

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Cite This Study

Elkhiri et al. (Fri,) studied this question.

synapsesocial.com/papers/69a3d6eaec16d51705d2d9d6 https://doi.org/https://doi.org/10.4134/bkms.b200359

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