This article is cited in 2 papers

Symbol of type and the Wilson theorem

S. A. Tyurin

Faculty of Regional Staff Training, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

Abstract: We introduce the notion of an element type for the field of residues modulo a prime number and study its role in factorial computation. We obtain an expression for its quantitative characteristic (the symbol of type) in terms of continued fractions and establish its connection with the Legendre symbol.

Keywords: number theory, finite fields, continued fractions.

UDC: 511.172

Received: 20.07.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:9, 39–45

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