Prime Factors of Dynamical Sequences
Abstract
Let f(t) be a rational function of degree at least 2 with rational coefficients. For a given rational number x0, define xn+1=f(xn) for each nonnegative integer n. If this sequence is not eventually periodic, then the difference xn+1-xn has a primitive prime factor for all sufficiently large n. This result provides a new proof of the infinitude of primes for each rational function f of degree at least 2.
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