Conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers

TL;DR

This paper presents numerous conjectures regarding congruences involving binomial coefficients and Apéry-like numbers, aiming to stimulate further research in this area.

Contribution

It introduces several new conjectures on congruences involving binomial coefficients and Apéry-like numbers, expanding the theoretical landscape.

Findings

Proposes multiple challenging conjectures on congruences.

Highlights the complexity of relationships between binomial coefficients and Apéry-like numbers.

Encourages future research to prove or disprove these conjectures.

Abstract

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.