Three-term arithmetic progressions of consecutive powerful numbers
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914540455723008 |
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| author | van Doorn, Wouter |
| author_facet | van Doorn, Wouter |
| contents | We show that infinitely many three-term arithmetic progressions $N, N+d, N+2d$ of powerful numbers exist with $d = 2\sqrt{N} + 1$. We further conjecture that infinitely many of these progressions consist of three consecutive terms in the sequence of powerful numbers, which would answer a question of Erdős in the negative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06697 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Three-term arithmetic progressions of consecutive powerful numbers van Doorn, Wouter Number Theory We show that infinitely many three-term arithmetic progressions $N, N+d, N+2d$ of powerful numbers exist with $d = 2\sqrt{N} + 1$. We further conjecture that infinitely many of these progressions consist of three consecutive terms in the sequence of powerful numbers, which would answer a question of Erdős in the negative. |
| title | Three-term arithmetic progressions of consecutive powerful numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.06697 |