Repetition of the last digits of a tetration of generic base

[Luknik]

Thank you James! I'll try to reduce those giant expressions \( \mod p^{n} \) , you're right, it is a pretty good idea in order to understand what's going on for all primes. Maybe it'll be useful to understand the \( \mod 10^{n} \) case, although \( 10^{n} = 2^{n}\cdot 5^{n} \) .. so of course it is a more complicated case. It's very interesting to have properties of giant number, it's like "controlling the infinity". I really hope we can figure out a solution to this amazing problem! But at the moment we have only a conjecture, which is not bad at all! Have a good day everybody.
Regards, Luca.