Definitive Proof of The abc Conjecture

EasyChair Preprint no. 2169, version 2

Abstract

In this paper, we consider the $abc$ conjecture. Firstly, we give an    elementary    proof that $c<3rad^2(abc)$. Secondly, the proof of the $abc$ conjecture is given for $\epsilon \geq 1$, then for $\epsilon \in ]0,1[$. We choose the constant $K(\epsilon)$ as $K(\epsilon)=\frac{3}{e}.e^{ \left(\frac{1}{\epsilon^2} \right)}$ for $0<\epsilon<1$ and $K(\epsilon)=3$ for $\epsilon \geq 1$. Some numerical examples are presented.

Keyphrases: elementary number theory, prime numbers, Real functions of one variable

@Booklet{EasyChair:2169,
  author = {Abdelmajid Ben Hadj Salem},
  title = {Definitive Proof of The abc Conjecture},
  howpublished = {EasyChair Preprint no. 2169},

  year = {EasyChair, 2020}}