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Creators/Authors contains: "Gassert, Alden T."

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  1. ; ; (, New York journal of mathematics)
    Let ϕ(x) = xd + c be an integral polynomial of degree at least 2, and consider the sequence (ϕn(0))n=0∞, which is the orbit of 0 under iteration by ϕ. Let Dd,c denote the set of positive integers n for which n | ϕn(0). We give a characterization of Dd,c in terms of a directed graph and describe a number of its properties, including its cardinality and the primes contained therein. In particular, we study the question of which primes p have the property that the orbit of 0 is a single p-cycle modulo p. We show that the set of such primes is finite when d is even, and conjecture that it is infinite when d is odd. 
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