On products of primes and almost primes in arithmetic progressions

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Abstract

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
Volume67
Issue number1
DOIs
Publication statusPublished - Sep 2013

Keywords

  • primes
  • almost primes
  • sieve method
  • exponential sums

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