Proof of some divisibility results on sums involving binomial coefficients

TL;DR

This paper proves four supercongruences involving binomial coefficient sums using Rodriguez-Villegas-Mortenson supercongruences, confirming conjectures by Sun and Guo about divisibility and integer-valued polynomials.

Contribution

It introduces new proofs of supercongruences on binomial sums and verifies a conjecture on integer-valued polynomials, expanding understanding of divisibility properties.

Findings

Proved four supercongruences on binomial sums

Confirmed a conjecture of Guo on integer-valued polynomials

Extended the application of Rodriguez-Villegas-Mortenson supercongruences

Abstract

By using the Rodriguez-Villegas-Mortenson supercongruences, we prove four supercongruences on sums involving binomial coefficients, which were originally conjectured by Sun. We also confirm a related conjecture of Guo on integer-valued polynomials.