On the relation between perfect powers and tetration frozen digits

Marco  Ripà

doi:10.59400/jam1771

On the relation between perfect powers and tetration frozen digits

Marco Ripà Independent Researcher, Rome, Italy

Article ID: 1771

1126 Views

DOI: https://doi.org/10.59400/jam1771

Keywords: congruence speed; convergence; perfect power; power tower; tetration

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.

References

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Published

2024-12-09

How to Cite

Ripà, M. (2024). On the relation between perfect powers and tetration frozen digits. Journal of AppliedMath, 2(5), 1771. https://doi.org/10.59400/jam1771

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Vol. 2 No. 5 (2024)

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