# On some problems of Harju concerning squarefree arithmetic progressions in infinite words

## TL;DR

This paper addresses open problems posed by Harju about the existence and properties of square-free arithmetic progressions in infinite words, providing solutions to two of these problems.

## Contribution

It solves two of Harju's open problems related to square-free arithmetic progressions in infinite words.

## Key findings

- Solved two of Harju's open problems.
- Established new results on square-free arithmetic progressions.
- Contributed to the theoretical understanding of infinite words.

## Abstract

In a recent paper, Harju posed three open problems concerning square-free arithmetic progressions in infinite words. In this note we solve two of them.