Polynomials with divisors of every degree

Details Polynomials with divisors of every degree Polynomials with divisors of every degree

2011-11-23

arxiv.org/abs/1111.5401v1

Mathematics

Number Theory

18 pages, to appear in the Journal of Number Theory

Scientific paper

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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