Sum of terms of recurrence sequences in the solution sets of generalized Pell equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917778858967040 |
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| author | Bhoi, Pritam Kumar Padhy, Rudranarayan Rout, Sudhansu Sekhar |
| author_facet | Bhoi, Pritam Kumar Padhy, Rudranarayan Rout, Sudhansu Sekhar |
| contents | Let $(X_{k})_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be the sequence of $X$ and $Y$-coordinates of the positive integer solutions $(x, y)$ of the equation $x^2 - dy^2 = t$. In this paper we completely describe those recurrence sequences such that sums of two terms recurrence sequences in the solution sets of generalized Pell equations are infinitely many. Further, we give an upper bound for the number of such terms when there are only finitely many of them. This work is motivated by the recent paper Hajdu and Sebestyén (Int. J. Number Theory 18 (2022), 1605-1612). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sum of terms of recurrence sequences in the solution sets of generalized Pell equations Bhoi, Pritam Kumar Padhy, Rudranarayan Rout, Sudhansu Sekhar Number Theory 11B37, 11D61, and 11D09 Let $(X_{k})_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be the sequence of $X$ and $Y$-coordinates of the positive integer solutions $(x, y)$ of the equation $x^2 - dy^2 = t$. In this paper we completely describe those recurrence sequences such that sums of two terms recurrence sequences in the solution sets of generalized Pell equations are infinitely many. Further, we give an upper bound for the number of such terms when there are only finitely many of them. This work is motivated by the recent paper Hajdu and Sebestyén (Int. J. Number Theory 18 (2022), 1605-1612). |
| title | Sum of terms of recurrence sequences in the solution sets of generalized Pell equations |
| topic | Number Theory 11B37, 11D61, and 11D09 |
| url | https://arxiv.org/abs/2403.18924 |