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arXiv · 2307.16616

Definition of the invariant and the relationship with the compounds numbers. Generalisation of the Euler theorem

Juan Hernandez-Toro
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Abstract

The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this theorem for all the values of $a^{\varphi(m)}$ where $0 < a < m {\pmod {m}}$ independently if a is co prime or not with m. As $a^{\varphi(m)+1} \equiv a$ if $m = a \cdot b$ and $GCD(a, b) = 1$. As the following steps, a new hypothesis is formulated regarding the substitution of the Totien function for an equivalent function that explains the Carmichael numbers. Keywords: Prime Numbers, Compound Numbers, Primality test, Euler theorem

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Juan Hernandez-Toro. 2023-07-31. Definition of the invariant and the relationship with the compounds numbers. Generalisation of the Euler theorem. https://arxiv.org/abs/2307.16616

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