Vol. 28, No. 3, 1969

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ISSN: 0030-8730
On a conjecture of Golomb

William H. Mills and Neal Zierler

Vol. 28 (1969), No. 3, 635–640
Abstract

On the basis of empirical evidence for n = 2,3,4, and 5 Golomb has conjectured that the degree of every irreducible factor of

F(x) = x2n+1 + x2n−1−1 +1

over GF(2) divides 6(n 1). We prove the stronger result that the degree of every irreducible factor of F(x) divides either 2(n 1) or 3(n 1), but not n 1.

Mathematical Subject Classification
Primary: 12.25
Milestones
Received: 8 June 1968
Published: 1 March 1969
Authors
William H. Mills
Neal Zierler