Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Consecutive numbers with the same Legendre symbol

Author: Zhi-Hong Sun
Journal: Proc. Amer. Math. Soc. 130 (2002), 2503-2507
MSC (2000): Primary 11A15; Secondary 11A07
Published electronically: April 17, 2002
MathSciNet review: 1900855
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $p$ be an odd prime, and $R_{p}$ be a complete set of residues $(\text{\rm mod} p)$. The goal of the paper is to determine all the values of $n (n\in R_{p})$ such that $\big (\frac{n}{p}\big ) = \big (\frac{n+1}{p}\big )$ or $\big (\frac{n-1}{p}\big )= \big (\frac{n}{p}\big ) =\big (\frac{n+1}{p}\big )$, where $\big (\frac{\cdot }{p}\big ) $ is the Legendre symbol.

References [Enhancements On Off] (What's this?)

  • [BE] B.C. Berndt and R.J. Evans, Sums of Gauss, Jacobi, and Jacobsthal, J. Number Theory 11 (1979), 349-398. MR 81j:10054
  • [BEW] B.C. Berndt, R.J. Evans and K.S. Williams, Gauss and Jacobi Sums, John Wiley $\&$ Sons, Inc., New York, Chichester, 1998, p. 58. MR 99d:11092
  • [D] H. Davenport, The Higher Arithmetic, 5th edition, Cambridge University Press, London, New York, 1982, pp. 74-76. MR 84a:10001
  • [J] E. Jacobsthal, Über die Darstellung der Primzahlen der Form $4n+1$ als Summe zweier Quadrate, J. Reine Angew. Math. 132 (1907), 238-245.
  • [S] Zhi-Hong Sun, Supplements to the theory of quartic residues, Acta Arith. 97 (2001), 361-377. MR 2002c:11007

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11A15, 11A07

Retrieve articles in all journals with MSC (2000): 11A15, 11A07

Additional Information

Zhi-Hong Sun
Affiliation: Department of Mathematics, Huaiyin Teachers College, Huaian, Jiangsu 223001, People’s Republic of China

Keywords: Prime, Legendre symbol
Received by editor(s): February 27, 2001
Published electronically: April 17, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society