## Definitive Tentative of a Proof of the \textit{abc} Conjecture

**Authors:** Abdelmajid Ben Hadj Salem

In this paper, we consider the $abc$ conjecture. Firstly, we give anelementaryproof 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.

**Comments:** 11 Pages. Submitted to the journal Inventiones Matemathicae

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### Submission history

[v1] 2020-01-06 14:00:37

[v2] 2020-01-08 02:22:57

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