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      Variations on a theme of Mirsky

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      Author(s)
      Akbal, Yıldırım
      Güloğlu, Ahmet
      Date
      2022-07-05
      Source Title
      International Journal of Number Theory
      Print ISSN
      1793-0421
      Electronic ISSN
      1793-7310
      Publisher
      World Scientific Publishing
      Volume
      19
      Issue
      1
      Pages
      1 - 39
      Language
      English
      Type
      Article
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      Abstract
      Let k and r be non-zero integers with r≥2. An integer is called r-free if it is not divisible by the rth power of a prime. A result of Mirsky states that there are infinitely many primes p such that p+k is r-free. In this paper, we study an additive Goldbach-type problem and prove two uniform distribution results using these primes. We also study certain properties of primes p such that p+a1,…,p+aℓ are simultaneously r-free, where a1,…,aℓ are non-zero integers and ℓ≥1 .
      Keywords
      Hardy–Littlewood circle method
      r-free shifted primes
      Goldbach-type additive problems
      Permalink
      http://hdl.handle.net/11693/111566
      Published Version (Please cite this version)
      https://doi.org/10.1142/S179304212350001X
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      • Department of Mathematics 712
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