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Publication Date:
24 01 2012
DOI:
10.1515/integ.2011.083

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Editor-in-Chief: Nathanson, Melvyn B. / Nešetril, Jaroslav / Pomerance, Carl

6 Issues per year

Mathematical Citation Quotient 2010: 0.20

Enumeration of Triangles in Quartic Residue Graphs

1Department of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC, USA

2Department of Mathematics, Armstrong Atlantic State University, Savannah, GA, USA

3Department of Mathematics, Armstrong Atlantic State University, Savannah, GA, USA

4Department of Mathematics, Armstrong Atlantic State University, Savannah, GA, USA

5Department of Mathematics, Armstrong Atlantic State University, Savannah, GA, USA

Citation Information: Integers. Volume 12, Issue 1, Pages 57–73, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: 10.1515/integ.2011.083, January 2012

Publication History:

Received: 10/10/2010;
Accepted: 19/07/2011;
Published Online: 27/02/2012

Abstract.

For a fixed prime p1(mod4), we define the corresponding quartic residue graph and determine the number of triangles contained in such a graph. Our computation requires us to compute the number of pairs of consecutive quartic residues modulo p via the evaluation of certain quartic Jacobi sums.

Keywords.: Reciprocity Laws; Paley Graphs; Jacobi Sums

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