On the relation between perfect powers and tetration frozen digits
Year: 2024
Type: article
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 having a constant congruence speed of c.
Source: Journal of AppliedMath
DOI: 10.59400/jam1771
Author: Marco Ripà
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4390850501