Article

An infinite family of cubics with emergent reducibility at depth 1

Published in: Quaestiones Mathematicae
Volume 40 , issue 1 , 2017 , pages: 13–16

DOI: 10.2989/16073606.2016.1259187

Author(s): Jason I. Preszler Learning Centers and Department of Mathematics and Statistics, USA

Keywords: Primary 11R09 , Secondary 37P05 , 11D25 , Primary 11R09 , Secondary 37P05 , 11D25

Abstract

A polynomial f (x) has emergent reducibility at depth n if f^◦k (x) is irreducible for 0 ≤ k ≤ n − 1 but f^◦n(x) is reducible. In this paper we prove that there are infinitely many irreducible cubics f ∈

[x] with f ◦f reducible by exhibiting a one parameter family with this property.

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Article

An infinite family of cubics with emergent reducibility at depth 1

Abstract

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