2021•arXiv (Cornell University)Open access

A new characterization of prime Fermat's numbers

Ahmed Bouzalmat, Ahmed Sani

Abstract

We give a new sufficient condition which allows to test primality of Fermat's numbers. This characterization uses uniquely values at most equal to tested Fermat number. The robustness of this result is due to a strict use of elementary arithmetic technical tools and it will be susceptible to open gates for revolutionary statement that all Fermat's numbers are all decomposable.

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Key concepts: Primality test, Fermat's Last Theorem, Fermat number, Mathematics, Characterization (materials science), Arithmetic, Discrete mathematics, Fermat's little theorem