On the Weakly Prime-Additive Numbers with Length 4
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866916959307694080 |
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| author | Leung, Wing Hong |
| author_facet | Leung, Wing Hong |
| contents | In 1992, Erd$ő$s and Hegyv$á$ri showed that for any prime p, there exist infinitely many length 3 weakly prime-additive numbers divisible by p. In 2018, Fang and Chen showed that for any positive integer m, there exists infinitely many length 3 weakly prime-additive numbers divisible by m if and only if 8 does not divide m. Under the assumption (*) of existence of a prime in certain arithmetic progression with prescribed primitive root, which is true under the Generalized Riemann Hypothesis (GRH), we show for any positive integer m, there exists infinitely many length 4 weakly prime-additive numbers divisible by m. We also present another related result analogous to the length 3 case shown by Fang and Chen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_10668 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the Weakly Prime-Additive Numbers with Length 4 Leung, Wing Hong Number Theory 11A07, 11A41 In 1992, Erd$ő$s and Hegyv$á$ri showed that for any prime p, there exist infinitely many length 3 weakly prime-additive numbers divisible by p. In 2018, Fang and Chen showed that for any positive integer m, there exists infinitely many length 3 weakly prime-additive numbers divisible by m if and only if 8 does not divide m. Under the assumption (*) of existence of a prime in certain arithmetic progression with prescribed primitive root, which is true under the Generalized Riemann Hypothesis (GRH), we show for any positive integer m, there exists infinitely many length 4 weakly prime-additive numbers divisible by m. We also present another related result analogous to the length 3 case shown by Fang and Chen. |
| title | On the Weakly Prime-Additive Numbers with Length 4 |
| topic | Number Theory 11A07, 11A41 |
| url | https://arxiv.org/abs/1903.10668 |