On products of primes and almost primes in arithmetic progressions

Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. This is a relaxed version of the still open question, studied by P. Erdo{double acute}s, A. M. Odlyzko and A. Sárközy, that corresponds to k = 1 (that is, to products of two primes).

Original languageEnglish
Pages (from-to)55-61
Number of pages7
JournalPeriodica Mathematica Hungarica
Issue number1
Publication statusPublished - Sept 2013


  • primes
  • almost primes
  • sieve method
  • exponential sums


Dive into the research topics of 'On products of primes and almost primes in arithmetic progressions'. Together they form a unique fingerprint.

Cite this