T-Fermat integers

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Tigran Hakobyan
DOI: 10.48550/arxiv.2603.00679
Cited by: 0
References: 1

Abstract

We introduce the concept of a T-Fermat integer, which generalizes the notion of a prime number. We show that any composite T-Fermat integer, if one exists, must be a Carmichael number. We prove several properties of T-Fermat integers and conjecture that there are infinitely many composite T-Fermat integers. Together with a further structural conjecture, this suggests a possible route toward proving the infinitude of primes $p$ such that $ω(p-1)\leq 2$.

Fields of Study & Subjects

Analytic Number Theory Research Algebraic Geometry and Number Theory Smarandache Functions and Recreational Number Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
28 February 2026
Language
EN
Document type
Preprint