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10^{f (n)} <10n + 1 <10^{f (n) +1}

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

September 20, 2021

functionalFunctional inequalityinequalitiesalgebra

Problem Statement

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.