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x_{2m} = x_m if x_1 = f(1), x_{n+1} = f(x_n)

Source: Czech and Slovak Olympiad 1988, National Round, Problem 1

September 13, 2024
funtionalgebraSequence

Problem Statement

Let ff be a representation of the set M={1,2,...,1988}M = \{1, 2,..., 1988\} into MM. For any natural nn, let x1=f(1)x_1 = f(1), xn+1=f(xn)x_{n+1} = f(x_n). Find out if there exists mm such that x2m=xmx_{2m} = x_m.
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