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In a recent paper, we considered integers n for which the polynomial x^n - 1has a divisor in Z[x] of every degree up to n, and we gave upper and lowerbounds for their distribution. In this paper, we consider those n for which thepolynomial x^n-1 has a divisor in F_p[x] of every degree up to n, where p is arational prime. Assuming the validity of the Generalized Riemann Hypothesis, weshow that such integers n have asymptotic density 0.

On the divisors of x^n-1 in F_p[x]