International Journal of Mathematics and Mathematical Sciences 
Volume 27 (2001), Issue 4, Pages 197-200
doi:10.1155/S0161171201011309

Constructing irreducible polynomials with prescribed level curves over finite fields

Mihai Caragiu1,2

 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

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}.