Abstract
In the paper “What is special about the divisors of 24?”, Sunil Chebolu proved an interesting result about the multiplication tables of from several different number theoretic points of view: all of the 1s in the multiplication table for are located on the main diagonal if and only if is a divisor of 24. Put another way, this theorem characterizes the positive integers with the property that the proportion of 1s on the diagonal is precisely 1. The present work is concerned with finding the positive integers for which there is a given fixed proportion of 1s on the diagonal. For example, when is prime, we prove that there exists a positive integer such that of the 1s lie on the diagonal of the multiplication table for if and only if is a Sophie Germain prime.
Citation
Karenna Genzlinger. Keir Lockridge. "Sophie Germain primes and involutions of $\mathbb{Z}_n^\times$." Involve 8 (4) 653 - 663, 2015. https://doi.org/10.2140/involve.2015.8.653
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