The abc Conjecture: The Proof of c<rad^2(abc)

EasyChair Preprint 3160

Abstract

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.

Keyphrases: Real functions of one variable, The prime counting function, elementary number theory

@booklet{EasyChair:3160,
  author    = {Abdelmajid Ben Hadj Salem},
  title     = {The abc Conjecture: The Proof of c<rad^2(abc)},
  howpublished = {EasyChair Preprint 3160},
  year      = {EasyChair, 2020}}