On the relation between perfect powers and tetration frozen digits
Authors/Creators
Description
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 \(c\).
Notes (English)
This version of the paper differs from the Journal of AppliedMath version (DOI: 10.59400/jam1771) only by the addition of Reference [12] and the citation of the OEIS sequence A379243, which was approved after the journal publication.
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Additional details
Related works
- Requires
- Journal article: 10.7546/nntdm.2021.27.4.43-61 (DOI)
- Journal article: 10.7546/nntdm.2022.28.3.441-457 (DOI)
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