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arXiv · 2602.00252

On the relation between perfect powers and tetration frozen digits

Marco Ripà
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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 $20$ 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 $c$.

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Marco Ripà. 2026-01-30. On the relation between perfect powers and tetration frozen digits. https://doi.org/10.59400/jam1771

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