Product of powers of distinct primes as sums of Fibonacci numbers
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918347294113792 |
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| author | Batte, Herbert Luca, Florian Ziegler, Volker |
| author_facet | Batte, Herbert Luca, Florian Ziegler, Volker |
| contents | Let $F_n$ be the $n$-th Fibonacci number. In this paper, we study the Diophantine equation $F_n+F_m=p^xq^y$ in nonnegative integers $n\ge m$, $x$ and $y$, where $p$ and $q$ are fixed distinct prime numbers. We determine all pairs of primes $(q,p)$ with $q\le \min\{1000,p\}$ such that the above equation has at least two solutions $(x,y)$ (and corresponding $m,n$) in positive integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17903 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Product of powers of distinct primes as sums of Fibonacci numbers Batte, Herbert Luca, Florian Ziegler, Volker Number Theory 11B39, 11D61, 11D45, 11Y50 Let $F_n$ be the $n$-th Fibonacci number. In this paper, we study the Diophantine equation $F_n+F_m=p^xq^y$ in nonnegative integers $n\ge m$, $x$ and $y$, where $p$ and $q$ are fixed distinct prime numbers. We determine all pairs of primes $(q,p)$ with $q\le \min\{1000,p\}$ such that the above equation has at least two solutions $(x,y)$ (and corresponding $m,n$) in positive integers. |
| title | Product of powers of distinct primes as sums of Fibonacci numbers |
| topic | Number Theory 11B39, 11D61, 11D45, 11Y50 |
| url | https://arxiv.org/abs/2602.17903 |