On products of primes and square-free integers in arithmetic progressions
Keywords:
Kloosterman sums, congruencesAbstract
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.