Further Extensions of Sury's Identity
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913105521410048 |
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| author | Dresden, Gregory Gao, Xiaoya |
| author_facet | Dresden, Gregory Gao, Xiaoya |
| contents | The equation commonly known as Sury's identity is a deceptively simple summation formula that connects the Lucas numbers, Fibonacci numbers, and powers of two. Many authors have given extensions and generalizations over the years; in this paper, we take a different approach that allows us to produce a good number of new summation formulas, all from elementary (but non-trivial) methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Further Extensions of Sury's Identity Dresden, Gregory Gao, Xiaoya Number Theory Combinatorics 11B39 The equation commonly known as Sury's identity is a deceptively simple summation formula that connects the Lucas numbers, Fibonacci numbers, and powers of two. Many authors have given extensions and generalizations over the years; in this paper, we take a different approach that allows us to produce a good number of new summation formulas, all from elementary (but non-trivial) methods. |
| title | Further Extensions of Sury's Identity |
| topic | Number Theory Combinatorics 11B39 |
| url | https://arxiv.org/abs/2512.12841 |