On weakly prime-additive numbers with length $4k+3$
If a positive integer $n$ has at least two distinct prime divisors and can be written as $n=p_1^{\alpha _1}+\dots +p_t^{\alpha _t}$, where $p_1<\dots 3$. The main result is summarized as follows: for any positive integers $m,t$ with $t\equiv 3 \pmod {4}$ and $t>3$, there exist infinitely many...
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| Language: | English |
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.555/ |
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| author | Fang, Jin-Hui Xue, Fang-Gang |
| author_facet | Fang, Jin-Hui Xue, Fang-Gang |
| author_sort | Fang, Jin-Hui |
| collection | DOAJ |
| description | If a positive integer $n$ has at least two distinct prime divisors and can be written as $n=p_1^{\alpha _1}+\dots +p_t^{\alpha _t}$, where $p_1<\dots 3$. The main result is summarized as follows: for any positive integers $m,t$ with $t\equiv 3 \pmod {4}$ and $t>3$, there exist infinitely many weakly prime-additive numbers $n$ with $m\mid n$ and $n=p_1^{\alpha _1}+\dots +p_{t}^{\alpha _{t}}$, where $p_1,\dots ,p_t$ are distinct prime divisors of $n$ and $\alpha _1,\dots ,\alpha _t$ are positive integers. |
| format | Article |
| id | doaj-art-f587c3b3fe1e40bea3c910563fd9e081 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-f587c3b3fe1e40bea3c910563fd9e0812025-02-07T11:19:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G327527810.5802/crmath.55510.5802/crmath.555On weakly prime-additive numbers with length $4k+3$Fang, Jin-Hui0Xue, Fang-Gang1School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R. ChinaNanjing University of Information Science & Technology, Nanjing 210044, P.R. ChinaIf a positive integer $n$ has at least two distinct prime divisors and can be written as $n=p_1^{\alpha _1}+\dots +p_t^{\alpha _t}$, where $p_1<\dots 3$. The main result is summarized as follows: for any positive integers $m,t$ with $t\equiv 3 \pmod {4}$ and $t>3$, there exist infinitely many weakly prime-additive numbers $n$ with $m\mid n$ and $n=p_1^{\alpha _1}+\dots +p_{t}^{\alpha _{t}}$, where $p_1,\dots ,p_t$ are distinct prime divisors of $n$ and $\alpha _1,\dots ,\alpha _t$ are positive integers.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.555/weakly prime-additive numbersDirichlet’s theoremthe Chinese remainder theorem |
| spellingShingle | Fang, Jin-Hui Xue, Fang-Gang On weakly prime-additive numbers with length $4k+3$ Comptes Rendus. Mathématique weakly prime-additive numbers Dirichlet’s theorem the Chinese remainder theorem |
| title | On weakly prime-additive numbers with length $4k+3$ |
| title_full | On weakly prime-additive numbers with length $4k+3$ |
| title_fullStr | On weakly prime-additive numbers with length $4k+3$ |
| title_full_unstemmed | On weakly prime-additive numbers with length $4k+3$ |
| title_short | On weakly prime-additive numbers with length $4k+3$ |
| title_sort | on weakly prime additive numbers with length 4k 3 |
| topic | weakly prime-additive numbers Dirichlet’s theorem the Chinese remainder theorem |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.555/ |
| work_keys_str_mv | AT fangjinhui onweaklyprimeadditivenumberswithlength4k3 AT xuefanggang onweaklyprimeadditivenumberswithlength4k3 |