The Extended Generating Function of the Radical of n and the abc-Conjecture

TL;DR

This paper introduces an extended generating series involving the radical of n, which leads to an identity that proves Bombieri's abc-Conjecture for specific sets of integers.

Contribution

It presents a novel two-variable generating series that establishes a new proof of Bombieri's abc-Conjecture for certain integer sets.

Findings

Proves Bombieri's abc-Conjecture for specific sets of integers.

Introduces a new two-variable generating series involving the radical of n.

Establishes an identity in the generating series that underpins the proof.

Abstract

An extended generating series of the radical of n, involving two variables, leads to an identity in said variables, which proves Bombieri's abc-Conjecture for certain sets of integers.