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A Generalization of Swan's Theorem

Harold M. Fredricksen, Alfred W. Hales and Melvin M. Sweet
Mathematics of Computation
Vol. 46, No. 173 (Jan., 1986), pp. 321-331
DOI: 10.2307/2008235
Stable URL: http://www.jstor.org/stable/2008235
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Generalization of Swan's Theorem
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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 $x^nf + g$ 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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