On a theorem of Kanold on odd perfect numbers
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929255728807936 |
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| author | Yamada, Tomohiro |
| author_facet | Yamada, Tomohiro |
| contents | We shall prove that if $N=p^αq_1^{2β_1} q_2^{2β_2} \cdots q_{r-1}^{2β_{r-1}}$ is an odd perfect number such that $p, q_1, \ldots, q_{r-1}$ are distinct primes, $p\equivα\equiv 1\mod{4}$ and $t$ divides $2β_i+1$ for all $i=1, 2, \ldots, r-1$, then $t^5$ divides $N$, improving an eighty-year old result of Kanold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17059 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a theorem of Kanold on odd perfect numbers Yamada, Tomohiro Number Theory Primary 11A25, Secondary 11A05 We shall prove that if $N=p^αq_1^{2β_1} q_2^{2β_2} \cdots q_{r-1}^{2β_{r-1}}$ is an odd perfect number such that $p, q_1, \ldots, q_{r-1}$ are distinct primes, $p\equivα\equiv 1\mod{4}$ and $t$ divides $2β_i+1$ for all $i=1, 2, \ldots, r-1$, then $t^5$ divides $N$, improving an eighty-year old result of Kanold. |
| title | On a theorem of Kanold on odd perfect numbers |
| topic | Number Theory Primary 11A25, Secondary 11A05 |
| url | https://arxiv.org/abs/2312.17059 |