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arXiv · 0903.1344

Prime Factors of Dynamical Sequences

Xander Faber·Andrew Granville
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Abstract

Let f(t) be a rational function of degree at least 2 with rational coefficients. For a given rational number x_0, define x_{n+1}=f(x_n) for each nonnegative integer n. If this sequence is not eventually periodic, then the difference x_{n+1}-x_n 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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Xander Faber, Andrew Granville. 2009-03-07. Prime Factors of Dynamical Sequences. https://arxiv.org/abs/0903.1344

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