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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A generalization of Swan's theorem


Authors: Harold M. Fredricksen, Alfred W. Hales and Melvin M. Sweet
Journal: Math. Comp. 46 (1986), 321-331
MSC: Primary 11T06
MathSciNet review: 815852
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Abstract: Let f and g denote polynomials over the two-element field. In this paper we show that the parity of the number of irreducible factors of $ {x^n}f + g$ is a periodic function of n, with period dividing eight times the period of the polynomial $ {f^2}(x(g/f)'- n(g/f))$. This can be considered a generalization of Swan's trinomial theorem [3].


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DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0815852-1
PII: S 0025-5718(1986)0815852-1
Article copyright: © Copyright 1986 American Mathematical Society