2022/10/01 by Hùng Việt Chu, Chu, Hung Viet, Kevin Huu Le +7
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2210.00363
openalex publication_date 2022/10/01 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
For each positive integer N, define S'N = \1 lt; d lt; √(N): d|N\ and L'N = \√(N) lt; d lt; N : d|N\. Recently, Chentouf characterized all positive integers N such that the set of small divisors \d≤ √(N): d|N\ satisfies a linear recurrence of order at most two. We nontrivially extend the result by excluding the trivial divisor 1 from consideration, which dramatically increases the analysis complexity. Our first result characterizes all positive integers N such that S'N satisfies a linear recurrence of order at most two. Moreover, our second result characterizes all positive N such that L'N satisfies a linear recurrence of order at most two, thus extending considerably a recent result that characterizes N with L'N being in an arithmetic progression.