New Congruences With the Generalized Catalan Numbers and Harmonic Numbers | Synapse
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,