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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2504.07040 |
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| _version_ | 1866917981541367808 |
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| author | Voutier, Paul M |
| author_facet | Voutier, Paul M |
| contents | We generalise our earlier work on the number of squares in binary recurrence sequences, $\left\{ y_{k} \right\}_{k \geq -\infty}$. In the notation of our previous papers, here we consider the case when $N_α$ is any negative integer and $y_{0}=b^{2}$ for any positive integer, $b$. We show that there are at most $4$ distinct squares with $y_{k}$ sufficiently large. This allows us to also show that there are at most $9$ distinct squares in such sequences when $b=1,2$ or $3$, or once $d$ is sufficiently large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds on the number of squares in recurrence sequences: arbitrary $b$, III Voutier, Paul M Number Theory We generalise our earlier work on the number of squares in binary recurrence sequences, $\left\{ y_{k} \right\}_{k \geq -\infty}$. In the notation of our previous papers, here we consider the case when $N_α$ is any negative integer and $y_{0}=b^{2}$ for any positive integer, $b$. We show that there are at most $4$ distinct squares with $y_{k}$ sufficiently large. This allows us to also show that there are at most $9$ distinct squares in such sequences when $b=1,2$ or $3$, or once $d$ is sufficiently large. |
| title | Bounds on the number of squares in recurrence sequences: arbitrary $b$, III |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.07040 |