Displaying similar documents to “The Bouniakowsky conjecture and the density of polynomial roots to prime moduli”

Plane Jacobian conjecture for simple polynomials

Nguyen Van Chau (2008)

Annales Polonici Mathematici

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A non-zero constant Jacobian polynomial map F=(P,Q):ℂ² → ℂ² has a polynomial inverse if the component P is a simple polynomial, i.e. its regular extension to a morphism p:X → ℙ¹ in a compactification X of ℂ² has the following property: the restriction of p to each irreducible component C of the compactification divisor D = X-ℂ² is of degree 0 or 1.

Prime divisors of linear recurrences and Artin's primitive root conjecture for number fields

Hans Roskam (2001)

Journal de théorie des nombres de Bordeaux

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Let S be a linear integer recurrent sequence of order k ≥ 3 , and define P S as the set of primes that divide at least one term of S . We give a heuristic approach to the problem whether P S has a natural density, and prove that part of our heuristics is correct. Under the assumption of a generalization of Artin’s primitive root conjecture, we find that P S has positive lower density for “generic” sequences S . Some numerical examples are included.