Wolstenholme Type Congruences and Framing of Rational 2-Functions

TL;DR

This paper explores the relationship between Wolstenholme's Theorem and the framing of rational 2-sequences, demonstrating that their generating functions can be extended to 3-sequences through a generalization.

Contribution

It introduces a new generalization of Wolstenholme's Theorem and shows how framing rational 2-sequences leads to 3-sequences, expanding understanding of sequence transformations.

Findings

Framing of rational 2-sequences results in 3-sequences.

Generalization of Wolstenholme's Theorem established.

Connecting sequence framing with sequence extension methods.

Abstract

We show that the framing of $2$-sequences whose generating functions are rational integrate to $3$-sequences. To do so, we give a generalization of Wolstenholme's Theorem.