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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 19, Pages 1175-1183

On the special solutions of an equation in a finite field

1Department of Mathematics, Weinan Teacher's College, Weinan, Shaanxi, China
2Research Center for Basic Science, Xi'an Jiaotong University, Xi'an, Shaanxi, China

Received 10 June 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The main purpose of this paper is to prove the following conclusion: let p be a prime large enough and let k be a fixed positive integer with 2k|p1. Then for any finite field Fp and any element 0cFp, there exist three generators x, y, and zFp such that xkyk+ykzk+xkzk=c.