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


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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


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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