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Lacunary Polynomial Compositions

2021/04/23 by Alessio Moscariello, Moscariello, Alessio
Computer Science · Mathematics · #11C08 #11R09 #12E05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2104.11704

openalex publication_date 2021/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some applications to Universal Hilbert Sets generated by closed forms of linear recurrence relations and to integer perfect powers having few digits in their representation in a given scale x ≥ 2 are provided.

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