A Generalization of Swan's Theorem
Harold M. Fredricksen, Alfred W. Hales, Melvin M. Sweet · Mathematics of Computation · 1986
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'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].