On products of primes and almost primes in arithmetic progressions
Volume 204 / 2022
Acta Arithmetica 204 (2022), 253-267
MSC: Primary 11N36; Secondary 11N25.
DOI: 10.4064/aa211215-2-6
Published online: 7 July 2022
Abstract
Let $q$ be a large positive integer and let $(a,q)=1$. We prove that there exist primes $p_1,p_2\le q$ and a number $n\le q$ with at most two prime factors such that $p_1p_2n\equiv a\pmod {q}$. This improves upon a result of Shparlinski (2018).
