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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.555/ |
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| Summary: | 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. |
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| ISSN: | 1778-3569 |