A generalization of Fermat-Catalan conjectureReport as inadecuate

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1 RIME ESSTT - Ecole Supérieure de Science et Technique de Tunis

Abstract : We begin with Beal equation or Fermat-Catalan $U^{c+2}=X^{a+2}+Y^{b+2}$ and establish two equivalent equations. We generalize the approach to all Fermat-Catalan equations which allows us to relate the problem to Matyasevich theorem. Our approach will lead us to propose a new conjecture concerning Fermat-Catalan equations. We propose also a proof of Beal conjecture.

Keywords : Conjecture Fermat-Catalan Diophantine equations Analysis Series Fourier series Conjecture.

Author: Jamel Ghannouchi -

Source: https://hal.archives-ouvertes.fr/


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