Several pseudorandom number generators based on the inversive congruential method have been designed as appealing alternatives to those based on the classical linear congruential method. This paper unveils the first functional graph structure of an inversive pseudorandom number generator over ring
$${\mathbb {Z}}_{p^{e}}$$
, resolving two foundational gaps: By transforming the generator into a second order linear congruential recurrence relation, we derives a complete and explicit expression of the least period of sequences generated from all initial states in the domain; The graph ...
