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arXiv · 1907.12057

Perfect powers in value sets and orbits of polynomials

Alina Ostafe·Lukas Pottmeyer·Igor E. Shparlinski
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Abstract

We show the finiteness of perfect powers in orbits of polynomial dynamical systems over an algebraic number field. We also obtain similar results for perfect powers represented by ratios of consecutive elements in orbits. Assuming the $abc$-Conjecture for number fields, we obtain a finiteness result for powers in ratios of arbitrary elements in orbits.

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Alina Ostafe, Lukas Pottmeyer, Igor E. Shparlinski. 2019-07-28. Perfect powers in value sets and orbits of polynomials. https://arxiv.org/abs/1907.12057

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