Variations on a theme of Mirsky

buir.contributor.authorGüloğlu, Ahmet
dc.citation.epage39en_US
dc.citation.issueNumber1en_US
dc.citation.spage1en_US
dc.citation.volumeNumber19en_US
dc.contributor.authorAkbal, Yıldırım
dc.contributor.authorGüloğlu, Ahmet
dc.coverage.spatialSingaporeen_US
dc.date.accessioned2023-02-21T07:23:56Z
dc.date.available2023-02-21T07:23:56Z
dc.date.issued2022-07-05
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractLet 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 .en_US
dc.identifier.doi10.1142/S179304212350001Xen_US
dc.identifier.eissn1793-7310
dc.identifier.issn1793-0421
dc.identifier.urihttp://hdl.handle.net/11693/111566
dc.language.isoEnglishen_US
dc.publisherWorld Scientific Publishingen_US
dc.relation.isversionofhttps://doi.org/10.1142/S179304212350001Xen_US
dc.source.titleInternational Journal of Number Theoryen_US
dc.subjectHardy–Littlewood circle methoden_US
dc.subjectr-free shifted primesen_US
dc.subjectGoldbach-type additive problemsen_US
dc.titleVariations on a theme of Mirskyen_US
dc.typeArticleen_US
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