Primes of the form $[{n}^c]$ with square-free $n$
UDC 621 Let $[\, \cdot\,]$ be the floor function. We show that if $1<c<\dfrac{3849}{3334},$ then there exist infinitely many prime numbers of the form $[n^c],$ where $n$ is square-free.
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| Date: | 2024 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7258 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865793847563386880 |
|---|---|
| author | Dimitrov, S. I. Dimitrov, S. I. |
| author_facet | Dimitrov, S. I. Dimitrov, S. I. |
| author_institution_txt_mv | [
{
"author": "S. I. Dimitrov",
"institution": "Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Bulgaria"
}
] |
| author_sort | Dimitrov, S. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:10Z |
| description | UDC 621
Let $[\, \cdot\,]$ be the floor function. We show that if $1<c<\dfrac{3849}{3334},$ then there exist infinitely many prime numbers of the form $[n^c],$ where $n$ is square-free. |
| doi_str_mv | 10.3842/umzh.v76i2.7258 |
| first_indexed | 2026-03-24T03:32:06Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7258 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:06Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-72582024-06-19T00:35:10Z Primes of the form $[{n}^c]$ with square-free $n$ Primes of the form $[{n}^c]$ with square-free $n$ Dimitrov, S. I. Dimitrov, S. I. Prime numbers $\cdot$ Square-free numbers $\cdot$ Exponential sums UDC 621 Let $[\, \cdot\,]$ be the floor function. We show that if $1<c<\dfrac{3849}{3334},$ then there exist infinitely many prime numbers of the form $[n^c],$ where $n$ is square-free. УДК 621 Прості числа вигляду $[{n}^c]$,  де $n$ не є квадратом Нехай $[\, \cdot\,]$ – ціла частина числа. Показано, що для $1<c<\dfrac{3849}{3334}$  існує нескінченно багато простих чисел вигляду $[n^c],$ де $n$ не є квадратом. Institute of Mathematics, NAS of Ukraine 2024-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7258 10.3842/umzh.v76i2.7258 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 2 (2024); 224-233 Український математичний журнал; Том 76 № 2 (2024); 224-233 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7258/9726 Copyright (c) 2024 Stoyan Dimitrov |
| spellingShingle | Dimitrov, S. I. Dimitrov, S. I. Primes of the form $[{n}^c]$ with square-free $n$ |
| title | Primes of the form $[{n}^c]$ with square-free $n$ |
| title_alt | Primes of the form $[{n}^c]$ with square-free $n$ |
| title_full | Primes of the form $[{n}^c]$ with square-free $n$ |
| title_fullStr | Primes of the form $[{n}^c]$ with square-free $n$ |
| title_full_unstemmed | Primes of the form $[{n}^c]$ with square-free $n$ |
| title_short | Primes of the form $[{n}^c]$ with square-free $n$ |
| title_sort | primes of the form $[{n}^c]$ with square-free $n$ |
| topic_facet | Prime numbers $\cdot$ Square-free numbers $\cdot$ Exponential sums |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7258 |
| work_keys_str_mv | AT dimitrovsi primesoftheformncwithsquarefreen AT dimitrovsi primesoftheformncwithsquarefreen |