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On Fail-Rolle polynomials with few roots
L. H. Gallardo
Received: November 11, 2008; Accepted: January 13, 2009
Abstract. A splitting polynomial in one variable over a field is Fail-Rolle if its formal derivative does not split over the same field. It is known that the finite fields with more than four elements are exactly the finite fields for which there are Fail-Rolle polynomials. We describe all Fail-Rolle polynomials with at most five roots over a finite field of even characteristic.
Keywords: quadratic forms; splitting polynomials; formal derivatives; finite fields; characteristic 2.
AMS Subject classification: Primary: 11T55, 11T06;
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