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2015 Sophie Germain primes and involutions of $\mathbb{Z}_n^\times$
Karenna Genzlinger, Keir Lockridge
Involve 8(4): 653-663 (2015). DOI: 10.2140/involve.2015.8.653


In the paper “What is special about the divisors of 24?”, Sunil Chebolu proved an interesting result about the multiplication tables of n from several different number theoretic points of view: all of the 1s in the multiplication table for n are located on the main diagonal if and only if n is a divisor of 24. Put another way, this theorem characterizes the positive integers n with the property that the proportion of 1s on the diagonal is precisely 1. The present work is concerned with finding the positive integers n for which there is a given fixed proportion of 1s on the diagonal. For example, when p is prime, we prove that there exists a positive integer n such that 1p of the 1s lie on the diagonal of the multiplication table for n if and only if p is a Sophie Germain prime.


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Karenna Genzlinger. Keir Lockridge. "Sophie Germain primes and involutions of $\mathbb{Z}_n^\times$." Involve 8 (4) 653 - 663, 2015.


Received: 9 June 2014; Revised: 9 June 2014; Accepted: 15 July 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1339.11004
MathSciNet: MR3366016
Digital Object Identifier: 10.2140/involve.2015.8.653

Primary: 11A41
Secondary: 16U60

Rights: Copyright © 2015 Mathematical Sciences Publishers


Vol.8 • No. 4 • 2015
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