On Stephan's conjectures concerning Pascal triangle modulo 2

TL;DR

This paper proves Stephan's conjectures related to Pascal's triangle modulo 2 and introduces a polynomial generalization, advancing understanding of combinatorial properties in modular arithmetic.

Contribution

The paper confirms Stephan's conjectures and extends them through a polynomial generalization, providing new insights into Pascal's triangle modulo 2.

Findings

Proved Stephan's conjectures about Pascal's triangle modulo 2

Developed a polynomial generalization of these conjectures

Enhanced understanding of combinatorial properties in modular arithmetic

Abstract

We prove a series of Stephan's conjectures concerning Pascal triangle modulo 2 and give a polynomial generalization.