# IJPAM: Volume 50, No. 4 (2009)

ON THE NUMBER OF SOLUTIONS OF THE EQUATION
IN FINITE FIELDS

Luo Yanmei, Zhao Zhengjun, Cao Xiwang
Department of Mathematics
Nanjing University of Aeronautics and Astronautics
Nanjing, 210016, P.R. CHINA
e-mail: ymluo@nuaa.edu.cn
e-mail: zzj0608115@126.com
e-mail: xwcao@nuaa.edu.cn

Abstract.Let be a finite field with elements, where is an odd prime. Let denote the number of solutions of the equation

in the finite field . We obtain the explicit formula for , where , , , . We also find explicit formulas for the number of solutions of , where or and .

Received: November 11, 2008

AMS Subject Classification: 11T06, 11T23

Key Words and Phrases: finite fields, solutions of equation, quadratic character

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 4