Vol. 32, No. 3, 1970

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Factorization of a special polynomial over a finite field

L. Carlitz

Vol. 32 (1970), No. 3, 603–614
Abstract

Let q = pz, where p is a prime and z 1, and put r = qn, n 1. Consider the polynomial

F (x) = x2r+1 + xr− 1 + 1.

Mills and Zierler proved that, for q = 2, the degree of every irreducible factor of F(x) over GF(2) divides either 2n or 3n.

Mathematical Subject Classification
Primary: 12.25
Milestones
Received: 14 July 1969
Published: 1 March 1970
Authors
L. Carlitz