On the Euler Function of Linearly Recurrence Sequences

2024/11/01 by Florian Luca, Makoko Campbell Manape · 1 citation
Physics and Astronomy · Mathematics · #Advanced Mathematical Theories and Applications #Mathematics and Applications #Advanced Mathematical Theories

paper · doi:10.1080/00150517.2024.12459548

Abstract

In this paper, we show that if (Un)n≥1 is any nondegenerate linearly recurrent sequence of integers whose general term is up to sign not a polynomial in n, then the inequality ∅(|Un|) ≥|U∅(n)| holds on a set of positive integers n of density 1, where ∅ is the Euler function. We show that the set of n ≤x for which the above inequality fails has counting function OU (x/log x).

Citations

• The zero multiplicity of linear recurrence sequences

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