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Mathematics of Computation

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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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Article copyright: © Copyright 1986 American Mathematical Society