The congruence speed formula
Number Theory
2022-08-05 v1
Abstract
We solve a few open problems related to a peculiar property of the integer tetration , which is the constancy of its congruence speed for any sufficiently large . Assuming radix- (the well-known decimal numeral system), we provide an explicit formula for the congruence speed of any that is not a multiple of . In particular, for any given , we prove to be true Rip\`a's conjecture on the smallest such that . Moreover, for any , we show the existence of infinitely many prime numbers such that .
Keywords
Cite
@article{arxiv.2208.02622,
title = {The congruence speed formula},
author = {Marco Ripà},
journal= {arXiv preprint arXiv:2208.02622},
year = {2022}
}
Comments
19 pages, 2 tables