On the divisors of xn-1 in Fp[x]
Abstract
In a recent paper, we considered integers n for which the polynomial xn - 1 has a divisor in Z[x] of every degree up to n, and we gave upper and lower bounds for their distribution. In this paper, we consider those n for which the polynomial xn-1 has a divisor in Fp[x] of every degree up to n, where p is a rational prime. Assuming the validity of the Generalized Riemann Hypothesis, we show that such integers n have asymptotic density 0.
0