Generalizations of a theorem about the binomial coefficient

TL;DR

This paper extends a known binomial coefficient theorem to arithmetic progressions and presents a slightly stronger version of Langevin's result, broadening the theorem's applicability.

Contribution

It generalizes an existing binomial coefficient theorem to arithmetic progressions and improves upon Langevin's result.

Findings

Extended theorem to arithmetic progressions

Provided a stronger version of Langevin's theorem

Broadened the theoretical understanding of binomial coefficients

Abstract

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].