Generalizations on a Problem of Saffari

TL;DR

This paper generalizes a classical problem on direct factor pairs to arbitrary finite families, providing a solution using Daboussi's method and discussing related open problems.

Contribution

It extends the original problem on direct factors to broader finite families and applies Daboussi's method for the solution.

Findings

Generalized Saffari's problem to finite families of direct factors

Provided a complete solution using Daboussi's method

Discussed related open problems in the area

Abstract

We provide a generalization of a problem first considered by Saffari and fully solved by Saffari, Erd\H{o}s and Vaughan on direct factor pairs, to arbitrary finite families of direct factors, and solve it using a method of Daboussi. We end with a few related open problems.