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Bundeswettbewerb Mathematik 1989 Problem 1.1

Source: Bundeswettbewerb Mathematik 1989 Round 1

September 25, 2022
rationaldecimal representationperiodicnumber theory

Problem Statement

For a given positive integer nn, let f(x)=xnf(x) =x^{n}. Is it possible for the decimal number 0.f(1)f(2)f(3)…0.f(1)f(2)f(3)\ldots to be rational? (Example: for n=2n=2, we are considering 0.1491625…0.1491625\ldots)
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