Akbal, YıldırımAkbal, YildirimGuloglu, Ahmet M.Mathematics2024-07-052024-07-05202301793-04211793-731010.1142/S179304212350001Xhttps://doi.org/10.1142/S179304212350001Xhttps://hdl.handle.net/20.500.14411/2113AKBAL, 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.eninfo:eu-repo/semantics/closedAccessHardy-Littlewood circle methodr-free shifted primesGoldbach-type additive problemsArticleQ3Q3191139WOS:000849372900001