# Some further results on squarefree arithmetic progressions in infinite words

## TL;DR

This paper resolves three open problems about the existence of squarefree arithmetic progressions in infinite words and presents additional related findings.

## Contribution

It provides solutions to previously open questions and introduces new results on squarefree arithmetic progressions in infinite words.

## Key findings

- Solved three open problems on squarefree arithmetic progressions.
- Proved new results related to infinite words and squarefree patterns.
- Enhanced understanding of the structure of squarefree sequences.

## Abstract

In a recent paper, one of us posed three open problems concerning squarefree arithmetic progressions in infinite words. In this note we solve these problems and prove some additional results.