# The $abc$ Conjecture implies the Weak Diversity Conjecture

## TL;DR

This paper demonstrates that assuming the abc Conjecture, a significant conjecture in number theory, leads to the validation of the Weak Diversity Conjecture proposed by Bilu and Luca.

## Contribution

It establishes a logical implication from the abc Conjecture to the Weak Diversity Conjecture, connecting two important conjectures in number theory.

## Key findings

- abc Conjecture implies Weak Diversity Conjecture
- Provides a new link between two major conjectures in number theory
- Strengthens the theoretical foundation for the Weak Diversity Conjecture

## Abstract

We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.