PreprintCC0arXiv
A characterization of Sophie Germain primes - II
Abstract
Let n≥ 4 be an even integer. We show that {1σ(1),2σ(2),…,nσ(n)} is a complete residue system modulo n for some permutation σ of {1,2,…,n} if and only if p:=n/2 is prime and p−1 is squarefree. This complements the results in [Int. J. Number Theory \textbf{14} (2018), 653--660], where an analogue characterization has been proved for odd integers.
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BibTeX
@misc{leonetti2026characterization,
title = {{A characterization of Sophie Germain primes - II}},
author = {Paolo Leonetti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20208},
eprint = {2609.20208},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20208},
note = {CC0},
}
RIS
TY - UNPB
TI - A characterization of Sophie Germain primes - II
AU - Paolo Leonetti
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20208
UR - https://arxiv.org/abs/2609.20208
AB - Let n≥ 4 be an even integer. We show that {1^σ(1),2^σ(2),…,n^σ(n)} is a complete residue system modulo n for some permutation σ of {1,2,…,n} if and only if p:=n/2 is prime and p−1 is squarefree. This complements the results in [Int. J. Number Theory \textbf{14} (2018), 653--660], where an analogue characterization has been proved for odd integers.
ER -