Work

A Note on Carmichael Numbers of the form $ N=(d+1)(3d+1)(4d+1)$

Year: 2026

Type: preprint

Abstract: We study integers of the form \[ N=(d+1)(3d+1)(4d+1). \] Using Korselt's criterion, we prove that, provided the three factors are prime, $N$ is a Carmichael number if and only if \[ d\equiv4\pmod{12}. \] We also show that the special case $d=2^m$ produces only $1105$ under the prime-factor hypothesis.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.24042

Author: Bensella, Hayat

Institution: University of Sciences and Technology Houari Boumediene

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223000106

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