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S = {1,2,3,4,5}, no of f : f : S \to S such that f ^{50}(x)= x

Source: Polish second round 1999 p5

January 19, 2020
combinatoricsfunctionfunctional equation

Problem Statement

Let S={1,2,3,4,5}S = \{1,2,3,4,5\}. Find the number of functions f:S→Sf : S \to S such that f50(x)=xf ^{50}(x)= x for all x∈Sx \in S.
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