The Bouniakowsky conjecture and the density of polynomial roots to prime moduli

TL;DR

This paper explores the connection between the Bouniakowsky conjecture and how densely polynomial roots occur modulo prime numbers, aiming to shed light on prime distribution related to polynomial values.

Contribution

It introduces a new theoretical link between the Bouniakowsky conjecture and the distribution density of polynomial roots modulo primes.

Findings

Established a theoretical connection between the conjecture and prime moduli roots density

Provided conditions under which polynomial roots are densely distributed mod primes

Suggested implications for prime number theory and polynomial value distribution

Abstract

We establish a result linking the Bouniakowsky conjecture and the density of polynomial roots to prime moduli.