Sum of terms of recurrence sequences and $S$-units in the solution sets of norm form equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912055777296384 |
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| author | N, Darsana Rout, S. S. |
| author_facet | N, Darsana Rout, S. S. |
| contents | In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations. Next, we give a finiteness result concerning solutions of norm form equations representable as sums of $S$-units with a fixed number of terms. To prove these results, we use a deep results concerning the finiteness of the solutions of polynomial-exponential equations and $S$-unit equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_01688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sum of terms of recurrence sequences and $S$-units in the solution sets of norm form equations N, Darsana Rout, S. S. Number Theory 11B37, 11D61, 11D57 In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations. Next, we give a finiteness result concerning solutions of norm form equations representable as sums of $S$-units with a fixed number of terms. To prove these results, we use a deep results concerning the finiteness of the solutions of polynomial-exponential equations and $S$-unit equations. |
| title | Sum of terms of recurrence sequences and $S$-units in the solution sets of norm form equations |
| topic | Number Theory 11B37, 11D61, 11D57 |
| url | https://arxiv.org/abs/2410.01688 |