Three integers arising from B\'{e}zout's identity and resultants of integer polynomials

TL;DR

This paper investigates three integers derived from Bézout's identity and polynomial resultants, establishing new divisibility relations and proposing conjectures based on computational evidence.

Contribution

It introduces novel divisibility relations among these integers and formulates two conjectures supported by computational experiments.

Findings

New divisibility relations among integers from Bézout's identity and resultants

Two conjectures proposed based on computational evidence

Enhanced understanding of algebraic properties of polynomial resultants

Abstract

In this paper, we study three integers arising naturally from B\'{e}zout's identity, the resultant and the reduced resultant of two coprime integer polynomials. We establish several new divisibility relations among them. We also pose two conjectures by making computations.