Work

Some results concerning odd numbers of the form 6k-1 and Fermat numbers

Year: 2026

Type: article

Abstract: In this work, one presents some results concerning odd numbers of the form 6k-1 and Fermat numbers using a new approach. Using this novel approach, one proves also that all odd numbers of the form 6k-1 and Fermat numbers are never perfect. In addition, one proves for the first time that all odd numbers of the form 6k-1 and Fermat numbers are never superperfect nor Descartes number, not quasiperfect and nor almost perfect. The case of near-perfect number is also considered in this study, where it is proved that all odd numbers of the form 6k-1 and Fermat numbers are never near-perfect.

Source: Galois Journal of Algebra

DOI: 10.65908/gja.2026.8392.1023

Authors: Abdelouahed Tounsi, Ismail Tounsi

Institutions: King Fahd University of Petroleum and Minerals, Université Djilali de Sidi Bel Abbès

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W7166724006

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