A note on three consecutive powerful numbers
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909555270615040 |
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| author | Chan, Tsz Ho |
| author_facet | Chan, Tsz Ho |
| contents | This note concerns the non-existence of three consecutive powerful numbers. We use Pell equations, elliptic curves, and second-order recurrences to show that there are no such triplets with the middle term a perfect cube and each of the other two having only a single prime factor raised to an odd power. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on three consecutive powerful numbers Chan, Tsz Ho Number Theory This note concerns the non-existence of three consecutive powerful numbers. We use Pell equations, elliptic curves, and second-order recurrences to show that there are no such triplets with the middle term a perfect cube and each of the other two having only a single prime factor raised to an odd power. |
| title | A note on three consecutive powerful numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.21485 |