New conjectures involving binomial coefficients and Ap\'ery-like numbers

TL;DR

This paper presents numerous conjectures regarding congruences of sums involving binomial coefficients and Apéry-like numbers modulo prime cubes, aiming to stimulate further research in number theory.

Contribution

It introduces many new conjectures on congruences for binomial and Apéry-like sums modulo p^3, expanding the landscape of related mathematical problems.

Findings

Proposes several challenging conjectures on congruences

Focuses on sums involving binomial coefficients and Apéry-like numbers

Addresses congruences modulo p^3 for odd primes

Abstract

In this paper, we pose lots of challenging conjectures on congruences for the sums involving binomial coefficients and Ap\'ery-like numbers modulo $p^3$, where $p$ is an odd prime.