A generalization of Swan’s theorem

Fredricksen, Harold M.; Hales, Alfred W.; Sweet, Melvin M.

doi:10.1090/S0025-5718-1986-0815852-1

A generalization of Swan’s theorem
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by Harold M. Fredricksen, Alfred W. Hales and Melvin M. Sweet PDF

Math. Comp. 46 (1986), 321-331 Request permission

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].

References

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