A Note on the least squarefree number in an arithmetic progression

Abstract

We prove an asymptotic formula for squarefree in arithmetic progressions with squarefree moduli, improving previous results by Prachar. The main tool is an estimate for counting solutions of a congruence inside a box that goes beyond what can be obtained by using the Weil bound.

6 pages, no figures

Cited by in corpus (3)

• On the variance of squarefree integers in short intervals and arithmetic progressions
• On smooth square-free numbers in arithmetic progressions
• Squarefree Integers in Arithmetic Progressions to Smooth Moduli