Powerful numbers and the ABC-conjecture

TL;DR

This paper explores the implications of the ABC-conjecture in number theory, focusing on its applications to the distribution of powerful numbers and illustrating its broad relevance.

Contribution

It introduces the ABC-conjecture and demonstrates its application to the study of powerful numbers, highlighting new connections in number theory.

Findings

The ABC-conjecture has significant implications for the distribution of powerful numbers.

Examples illustrate how the conjecture influences various areas in number theory.

Abstract

The $abc$ conjecture is a very deep concept in number theory with wide application to many areas of number theory. In this article we introduce the conjecture and give examples of its applications. In particular we apply the $abc$ conjecture to the location of powerful numbers.