Variations on a question concerning the degrees of divisors of xn-1
Abstract
In this paper, we examine a natural question concerning the divisors of the polynomial xn-1: "How often does xn-1 have a divisor of every degree between 1 and n?" In a previous paper, we considered the situation when xn-1 is factored in Z[x]. In this paper, we replace Z[x] with Fp[x], where p is an arbitrary-but-fixed prime. We also consider those n where this condition holds for all p.
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