Akbal,Y.Güloǧlu,A.M.Mathematics2024-07-052024-07-05202301793-042110.1142/S179304212350001X2-s2.0-85133913564https://doi.org/10.1142/S179304212350001XAKBAL, YILDIRIM/0000-0003-2138-4050Let 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. © 2023 World Scientific Publishing Company.eninfo:eu-repo/semantics/closedAccessGoldbach-type additive problemsHardy-Littlewood circle methodr -free shifted primesArticleQ3Q3191139WOS:000849372900001