A self-contained statement of a constant congruence speed identity characterizing integer tetration in numeral systems with radix \ (r > 2\). The central formula is \ (Vb^r ( (k r^t + 1 + r^t - ᵣ (c) 1) ᶜ) = t\) and it holds for all integers \ (b > 1\), \ (c > 1\), \ (k 0\), and \ (t > ᵣ (c) + 1\), for every squarefree integer \ (r > 2\), and also for most pairs \ ( (r, c) \) with positive non-squarefree integer \ (r\). Here \ (ᵣ (c) \) denotes the largest integer \ (m\) such that \ (rᵐ c\), and \ (rad (r) \) is the product of the distinct prime factors of \ (r\). A Python verification tool numerically confirming the stated (constant) congruence speed for the admissible parameter ranges is provided as a supplementary. py file (Version 3) in this Zenodo record: https: //doi. org/10. 5281/zenodo. 17982198
Marco Ripà (2025) studied this question.