A new characterization of prime Fermat's numbers
Ahmed Bouzalmat, Ahmed Sani
TL;DR
This paper introduces a new elementary arithmetic-based criterion for testing the primality of Fermat's numbers, potentially paving the way for proving their composability or primality.
Contribution
It presents a novel sufficient condition for Fermat number primality that relies on elementary arithmetic properties, offering a new approach to this longstanding problem.
Findings
Provides a new primality test criterion for Fermat's numbers
Uses elementary arithmetic tools for characterization
Suggests potential for proving all Fermat numbers are composite
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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Taxonomy
TopicsHistory and Theory of Mathematics · Mathematics and Applications · Algebraic Geometry and Number Theory