When the Nontrivial, Small Divisors of a Natural Number are in Arithmetic Progression

2020/01/20 by Hùng Việt Chu, Hung Viet Chu, Chu, Hung Viet
Mathematics · #11B25 #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #math.NT #msc:11B25

paper · pdf · doi:10.48550/arxiv.2001.08634

8 pages. Edited according to anonymous referees' suggestions. To appear in Quaestiones Mathematicae

openalex publication_date 2020/01/20 · arxiv created 2021/06/04 · arxiv updated 2021/06/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Iannucci considered the positive divisors of a natural number n that do not exceed √(n) and found all forms of numbers whose such divisors are in arithmetic progression. In this paper, we generalize Iannucci's result by excluding the trivial divisors 1 and √(n) (when n is a square). Surprisingly, the length of our arithmetic progression cannot exceed 5.

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