# On products of primes and square-free integers in arithmetic progressions

### From NZJM

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**New Zealand Journal of Mathematics**

**Vol.** 50, (2020), **Pages** 93-99

**Kam Hung Yau**

Department of Pure Mathematics University of New South Wales Sydney NSW 2052 Australia

mailto:kamhungyau.math@gmail.com

**Abstract** We obtain an asymptotic formula for the number of ways to represent every reduced residue class as a product of a prime and square-free integer. This may be considered as a relaxed version of a conjecture of Erd\"os, Odlyzko, and S\'ark\"ozy.

**Keywords** Kloosterman sums, congruences.

**Classification** (MSC2000) 11L05, 11A07.

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