Browsing by Subject "Goldbach-type additive problems"

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    Variations on a theme of Mirsky
    (World Scientific Publishing, 2022-07-05) Akbal, Yıldırım; Güloğlu, Ahmet
    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 .