Variations on a Theme of Mirsky

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2023

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World Scientific

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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. © 2023 World Scientific Publishing Company.

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AKBAL, YILDIRIM/0000-0003-2138-4050
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Keywords

Goldbach-type additive problems, Hardy-Littlewood circle method, r -free shifted primes

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0

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Q3

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Q3

Source

International Journal of Number Theory

Volume

19

Issue

1

Start Page

1

End Page

39

URI

https://doi.org/10.1142/S179304212350001X

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