PreprintCC BY 4.0arXiv
A Note on Carmichael Numbers of the form $ N=(d+1)(3d+1)(4d+1)$
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≡4pmod12. We also show that the special case d=2m produces only $1105$ under the prime-factor hypothesis.
Related
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BibTeX
@misc{bensella2026note,
title = {{A Note on Carmichael Numbers of the form $ N=(d+1)(3d+1)(4d+1)$}},
author = {Hayat Bensella},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24042},
eprint = {2610.24042},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24042},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Note on Carmichael Numbers of the form $ N=(d+1)(3d+1)(4d+1)$
AU - Hayat Bensella
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24042
UR - https://arxiv.org/abs/2610.24042
AB - 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≡4pmod12. We also show that the special case d=2^m produces only $1105$ under the prime-factor hypothesis.
ER -