The congruence of Wolstenholme and generalized binomial coefficients related to Lucas sequences

TL;DR

This paper explores generalized binomial coefficients based on Lucas sequences to establish new congruences that extend Wolstenholme's classical result and related stronger congruences.

Contribution

It introduces a framework for generalized binomial coefficients linked to Lucas sequences and derives new congruences extending classical Wolstenholme results.

Findings

Established congruences generalizing Wolstenholme's theorem

Derived stronger congruences related to Lucas sequences

Connected binomial coefficients with Lucas sequence properties

Abstract

Using generalized binomial coefficients with respect to fundamental Lucas sequences we establish congruences that generalize the classical congruence of Wolstenholme and other related stronger congruences.