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This paper investigates the behavior of the last digits of a tetration ofgeneric base. In fact, last digits of a tetration are the same starting from acertain hyper-exponent and in order to compute them we reduce those expressions$\mod 10^{n}$. Very surprisingly (although unproved) I think that therepetition of the last digits depend on the residue $\mod 10$ of the base andon the exponents of a particular way to express that base. Then I'll discussabout the results and I'll show different tables and examples in order tosupport my conjecture. We are very near to a proof for a formula which findsthe minimum hyper-exponent $u$ of a tetration with a generic base $q$ such thatthe last $n$ digits of the tetration starting from the $u$-th one are the same.

Observations regarding the repetition of the last digits of a tetration of generic base