| On the Number of Solutions of Certain Equations over Finite Fields |
| Received:September 12, 2008 Revised:January 05, 2009 |
| Key Words:
Finite fields solutions of equation multiplicative character inclusion-exclusion principle.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10971205; 10771100). |
| Author Name | Affiliation | | Zheng Jun ZHAO | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Jiangsu 211100, P. R. China | | Xi Wang CAO | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Jiangsu 211100, P. R. China
Department of Mathematics, LMIB of Ministry of Education, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China |
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| Abstract: |
| Let $\F_q$ be a finite field with $q=p^f$ elements, where $p$ is an odd prime. Let $N(a_1x_1^2 \cdots a_nx_n^2=bx_1\cdots x_s)$ denote the number of solutions $(x_1,\ldots,x_n)$ of the equation $a_1x_1^2 \cdots a_nx_n^2=bx_1\cdots x_s$ in $\F_q^n$, where $n>5$, $s5$, $3\leq s |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.002 |
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