Let n ≥ 5 be an odd integer. It is shown that {1σ(1),...,nσ(n)} is a complete residue system modulo n for some permutation σ of {1,...,n} if and only if 1 2(n - 1) is a Sophie Germain prime. Partial results are obtained also for the case n even.
A characterization of Sophie Germain primes
Leonetti P
2018-01-01
Abstract
Let n ≥ 5 be an odd integer. It is shown that {1σ(1),...,nσ(n)} is a complete residue system modulo n for some permutation σ of {1,...,n} if and only if 1 2(n - 1) is a Sophie Germain prime. Partial results are obtained also for the case n even.
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