Sums of three Fibonacci numbers as concatenations of three repdigits in base $b$
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918351368880128 |
|---|---|
| author | Dagou, Passimzouwé Tiebekabe, Pagdame Adédji, Kouèssi Norbert Tchariè, Kokou |
| author_facet | Dagou, Passimzouwé Tiebekabe, Pagdame Adédji, Kouèssi Norbert Tchariè, Kokou |
| contents | In this paper, we investigate sums of three Fibonacci numbers that can be expressed as concatenations of three repdigits in base $b$, where $b\ge 2$ is an integer. We prove that for bases $2\le b\le 10$, only finitely many such sums exist, and we determine all of them explicitly. Among these solutions, the largest occurs for $b=4$ and is given by $$ F_{42}+F_{29}+F_{20}=268435290=\overline{33333333331122}_4. $$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sums of three Fibonacci numbers as concatenations of three repdigits in base $b$ Dagou, Passimzouwé Tiebekabe, Pagdame Adédji, Kouèssi Norbert Tchariè, Kokou General Mathematics In this paper, we investigate sums of three Fibonacci numbers that can be expressed as concatenations of three repdigits in base $b$, where $b\ge 2$ is an integer. We prove that for bases $2\le b\le 10$, only finitely many such sums exist, and we determine all of them explicitly. Among these solutions, the largest occurs for $b=4$ and is given by $$ F_{42}+F_{29}+F_{20}=268435290=\overline{33333333331122}_4. $$ |
| title | Sums of three Fibonacci numbers as concatenations of three repdigits in base $b$ |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2602.20201 |