Polynomials with divisors of every degree

Published 23 Nov 2011 in math.NT | (1111.5401v1)

Abstract: We consider polynomials of the form t^n-1 and determine when members of this family have a divisor of every degree in Z[t]. With F(x) defined to be the number of such integers up to x, we prove the existence of two positive constants c_1 and c_2 such that $$c_1 x/(log x) \leq F(x) \leq c_2 x/(log x).$$

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Authors (1)

Lola Thompson

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