The $abc$ Conjecture: the Proof of $c

Authors: Abdelmajid Ben Hadj Salem

In this note, I present a very elementary proof of the conjecture $c<rad^2(abc)$ that constitutes the key to resolve the $abc$ conjecture. The method concerns the comparison of the number of primes of $c$ and $rad^2(abc)$ for large $a,b,c$ using the prime counting function $\pi(x)$ giving the number of primes $\leq x$. Some numerical examples are given.

Comments: 9 Pages. Submitted to the journal Annals of Mathematics.

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[v1] 2020-04-07 16:11:23

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