Power-free values, repulsion between points, differing beliefs and the existence of error

TL;DR

This paper investigates the distribution of prime values of cubic polynomials, showing that infinitely many primes p exist for which f(p) is square-free, highlighting a significant number-theoretic property.

Contribution

It establishes the existence of infinitely many primes p such that f(p) is square-free for cubic polynomials, advancing understanding of prime values of polynomial functions.

Findings

Infinitely many primes p with f(p) square-free for cubic polynomials

Supports conjectures on prime values of polynomial functions

Provides new insights into the distribution of polynomial prime values

Abstract

Let f be a cubic polynomial. Then there are infinitely many primes p such that f(p) is square-free.