Congruences for sums involving \binomrkk

2025/05/14 by Mattarei, Sandro, Tauraso, Roberto
#05A15 (Secondary) #11A07 (Primary) 05A10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.09849

Abstract

We primarily investigate congruences modulo p for finite sums of the form ∑_k\binomrkkx^k/k over the ranges 0

Citations

• From generating series to polynomial congruences
• Open Conjectures on Congruences
• Various congruences involving binomial coefficients and higher-order Catalan numbers

Related

• Congruences for partial sums of the generating series for \binom3kk
• Congruences involving the reciprocals of central binomial coefficients
• Congruences involving \binom4k2k and \binom3kk
• Elementary proof of congruences involving sum of binomial coefficients
• Congruences of multiple sums involving invariant sequences under binomial transform