On the relation between perfect powers and tetration frozen digits
Abstract
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 and the number of digits frozen by these special tetration bases, in radix-, for any unit increment of the hyperexponent. In particular, given any positive integer , we constructively prove the existence of infinitely many -th perfect powers that have a constant congruence speed of .
Keywords
Cite
@article{arxiv.2602.00252,
title = {On the relation between perfect powers and tetration frozen digits},
author = {Marco Ripà},
journal= {arXiv preprint arXiv:2602.00252},
year = {2026}
}
Comments
9 pages. This version of the paper differs from the journal version only by the addition of Reference [12] and the citation of the OEIS sequence A379243, which was approved after the journal publication