  In a recent paper, we considered integers n for which the polynomial x^n - 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 x^n-1 has a divisor in F_p[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.
