A Note on Values of Beatty Sequences That Are Free of Large Prime Factors

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2020

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Ars Polona-ruch

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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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Let alpha and beta be fixed real numbers and suppose that alpha > 1 is irrational and of finite type. We study values of the non-homogeneous Beatty sequence {left perpendicular alpha n + beta right perpendicular}(n=1)(infinity)that are free of large prime factors, where left perpendicularxright perpendicular is the largest integer not exceeding x.

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Beatty sequences, exponential sums, friable numbers

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Q4

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160

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1

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53

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63

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https://doi.org/10.4064/cm7715-2-2019
 https://hdl.handle.net/20.500.14411/3408

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