Download PDFOpen PDF in browserCurrent versionDefinitive Proof of The abc ConjectureEasyChair Preprint 2169, version 19 pages•Date: December 16, 2019AbstractIn this paper, we consider the $abc$ conjecture. Firstly, we give an elementary proof of the conjecture $c<rad^2(abc)$. 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 $K(\epsilon)=e^{\ds \left(\frac{1}{\epsilon^2} \right)}$. Some numerical examples are presented. Keyphrases: Real functions of one variable, elementary number theory, prime numbers
