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Enumeration of Triangles in Quartic Residue Graphs

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Published/Copyright: January 24, 2012
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Integers
From the journal Volume 12 Issue 1

Abstract.

For a fixed prime p≡1(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
Received: 2010-10-10
Accepted: 2011-07-19
Published Online: 2012-01-24
Published in Print: 2012-February

© 2012 by Walter de Gruyter Berlin Boston

Articles in the same Issue

  1. Prelims
  2. Selmer's Multiplicative Algorithm
  3. Lucas Numbers and Determinants
  4. A Combinatorial Proof of Guo's Multi-Generalization of Munarini's Identity
  5. Enumeration of Triangles in Quartic Residue Graphs
  6. A remark on the Boros–Moll Sequence
  7. A Relation Between Triangular Numbers and Prime Numbers
  8. Some Remarks on a Paper of V. A. Liskovets
  9. A Combinatorial Proof of a Recursive Formula for Multipartitions
  10. Aliquot Cycles of Repdigits
  11. Digital Sums and Functional Equations
https://doi.org/10.1515/integ.2011.083
Keywords for this article
Reciprocity Laws; Paley Graphs; Jacobi Sums

Articles in the same Issue

  1. Prelims
  2. Selmer's Multiplicative Algorithm
  3. Lucas Numbers and Determinants
  4. A Combinatorial Proof of Guo's Multi-Generalization of Munarini's Identity
  5. Enumeration of Triangles in Quartic Residue Graphs
  6. A remark on the Boros–Moll Sequence
  7. A Relation Between Triangular Numbers and Prime Numbers
  8. Some Remarks on a Paper of V. A. Liskovets
  9. A Combinatorial Proof of a Recursive Formula for Multipartitions
  10. Aliquot Cycles of Repdigits
  11. Digital Sums and Functional Equations
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