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International Journal of Mathematics and Mathematical Sciences
Volume 27, Issue 4, Pages 197-200
http://dx.doi.org/10.1155/S0161171201011309

Constructing irreducible polynomials with prescribed level curves over finite fields

1The Institute of Mathematics at Bucharest, P.O. Box 1-764, RO-70700, Romania
2Department of Mathematics, Ohio Northern University, Ada 45810, OH, USA

Received 14 January 2001; Revised 28 March 2001

Copyright © 2001 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.

Abstract

We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y)GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)GF(q)2|P(x,y)=c}.