Some properties of elements of the prime field

S. A. Tyurin

Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Ave., Nizhni Novgorod, 603950 Russia

Abstract: We obtain some properties of primitive roots in the groups of residue class modulo prime number, in particular, Fermat primes and Sophie Germain primes. We also obtain some formulas for computation of products of elements in some subsets of the prime field of positive characteristic.

Keywords: prime field, Fermat primes, Sophie Germain primes.

UDC: 511.172

Received: 13.01.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:8, 52–59

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