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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2504.20286 |
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| _version_ | 1866912352912277504 |
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| author | Bustos, Lucas Chu, Hung Viet Kim, Minchae Lee, Uihyeon Shankar, Shreya Tresch, Garrett |
| author_facet | Bustos, Lucas Chu, Hung Viet Kim, Minchae Lee, Uihyeon Shankar, Shreya Tresch, Garrett |
| contents | Zeckendorf's theorem states that every positive integer can be uniquely decomposed into nonadjacent Fibonacci numbers. On the other hand, Chung and Graham proved that every positive integer can be uniquely written as a sum of even-indexed Fibonacci numbers with coefficients $0,1$, or $2$ such that between two coefficients $2$, there is a coefficient $0$. For each $k\ge 1$, we find the set of all positive integers having $F_{2k}$ in both of their Zeckendorf and Chung-Graham decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integers Having $F_{2k}$ in Both Zeckendorf and Chung-Graham Decompositions Bustos, Lucas Chu, Hung Viet Kim, Minchae Lee, Uihyeon Shankar, Shreya Tresch, Garrett Number Theory 11B39 Zeckendorf's theorem states that every positive integer can be uniquely decomposed into nonadjacent Fibonacci numbers. On the other hand, Chung and Graham proved that every positive integer can be uniquely written as a sum of even-indexed Fibonacci numbers with coefficients $0,1$, or $2$ such that between two coefficients $2$, there is a coefficient $0$. For each $k\ge 1$, we find the set of all positive integers having $F_{2k}$ in both of their Zeckendorf and Chung-Graham decompositions. |
| title | Integers Having $F_{2k}$ in Both Zeckendorf and Chung-Graham Decompositions |
| topic | Number Theory 11B39 |
| url | https://arxiv.org/abs/2504.20286 |