Research Article

When the nontrivial, small divisors of a natural number are in arithmetic progression

Published in: Quaestiones Mathematicae
Volume 45 , issue 6 , 2022 , pages: 969–977

DOI: 10.2989/16073606.2021.1925369

Author(s): Hùng Việt Chu , USA

Keywords: Primary: 11B25 , Primary: 11B25

Abstract

Iannucci considered the positive divisors of a natural number n that do not exceed 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 (when n is a square). Surprisingly, the length of our arithmetic progression cannot exceed 5.

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