Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 3.4

Tags: functional, Functional inequality, inequalities, algebra



Determine if there exists a function f: $N^*\to N^*$ that satisfies that for all $n \in N^*$, $$10^{f (n)} <10n + 1 <10^{f (n) +1}.$$Justify your answer. Note: $N^*$ denotes the set of positive integers.