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01.On Even Integers Not of the Form 2k + σ(m) (pp. 263-268)
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The Irreducibility of Weighted Sums of Polynomials whose Irreducible Factors are Cyclotomic (pp. 225-236) $45.00
Authors:  Carrie Finch and Lenny Jones
Abstract:
For any positive integer n, we define the polynomial γn (x):= Σni=0xi. For any integer k ≥ 2, let S = {n1,n2, . . . ,nk} be a set of integers such that 0 < n1 < n2 < < nk, and define the polynomial Γw(s)(x) := Σki=1εixwiγ ni(x), where each wi is a nonnegative integer and ε2 ∈ {−1,1}. Based solely on the integers wi and ni, we give sufficient conditions in all cases for the reducibility over ℚ of Γw(s)(x), and necessary conditions, under suitable restrictions, when εi=1 and wi=0 for all i, and when k=2 with ε1 = ε2 = 1, and with exactly one of w1 and w2 equal to zero. In this second case, our conditions improve existing results in certain situations. 


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The Irreducibility of Weighted Sums of Polynomials whose Irreducible Factors are Cyclotomic (pp. 225-236)