The number of abc-equations c^n=a+b stisfying the strong abc-conjecture

TL;DR

This paper proves that the frequency of abc equations of the form c^n = a + b satisfying the strong abc-conjecture approaches half of phi(c^n) as n tends to infinity.

Contribution

It establishes an asymptotic density result for abc equations satisfying the strong abc-conjecture as n increases.

Findings

Frequency of abc equations c^n = a + b satisfying the strong abc-conjecture approaches half of phi(c^n) for large n.

Provides asymptotic density result related to the strong abc-conjecture.

Enhances understanding of the distribution of abc equations in number theory.

Abstract

We prove that the frequency of abc equations c^n = a+b satisfying the strong abc - conjecture is phi(c^n)/2+o(phi(c^n)/2), for n going to infinity.