On a multiplicative hybrid problem over almost-primes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910712856576000 |
|---|---|
| author | Zhao, Yuetong Zhai, Wenguang |
| author_facet | Zhao, Yuetong Zhai, Wenguang |
| contents | Let N be a large enough natural number, A and B be subsets of {N+1, ... , 2N}. In this paper, we prove that there exists integers a, b with a belongs to A, b belongs to B such that
ab=P_k^2 + O(P_k^{1-c}),
where 0<c<1/2 and P_k denotes an almost-prime with at most k prime factors, counted with multiplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a multiplicative hybrid problem over almost-primes Zhao, Yuetong Zhai, Wenguang Number Theory Let N be a large enough natural number, A and B be subsets of {N+1, ... , 2N}. In this paper, we prove that there exists integers a, b with a belongs to A, b belongs to B such that ab=P_k^2 + O(P_k^{1-c}), where 0<c<1/2 and P_k denotes an almost-prime with at most k prime factors, counted with multiplicity. |
| title | On a multiplicative hybrid problem over almost-primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.16069 |