On the relation between perfect powers and tetration frozen digits
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912863881265152 |
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| author | Ripà, Marco |
| author_facet | Ripà, Marco |
| contents | This paper provides a link between integer exponentiation and integer tetration since it is devoted to introducing some peculiar sets of perfect powers characterized by any given value of their constant congruence speed, revealing a fascinating relation between the degree of every perfect power belonging to any congruence class modulo $20$ and the number of digits frozen by these special tetration bases, in radix-$10$, for any unit increment of the hyperexponent. In particular, given any positive integer $c$, we constructively prove the existence of infinitely many $c$-th perfect powers that have a constant congruence speed of $c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the relation between perfect powers and tetration frozen digits Ripà, Marco General Mathematics 11A07, 11A15 This paper provides a link between integer exponentiation and integer tetration since it is devoted to introducing some peculiar sets of perfect powers characterized by any given value of their constant congruence speed, revealing a fascinating relation between the degree of every perfect power belonging to any congruence class modulo $20$ and the number of digits frozen by these special tetration bases, in radix-$10$, for any unit increment of the hyperexponent. In particular, given any positive integer $c$, we constructively prove the existence of infinitely many $c$-th perfect powers that have a constant congruence speed of $c$. |
| title | On the relation between perfect powers and tetration frozen digits |
| topic | General Mathematics 11A07, 11A15 |
| url | https://arxiv.org/abs/2602.00252 |