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f(f(x)) = x, |f(x) - x| \ge 2, f : T\to ={1,2,...,10}

Source: KJMO 2007 p6

May 2, 2019
algebrabijective functionfunctional equationfunction

Problem Statement

Let T={1,2,...,10}T = \{1,2,...,10\}. Find the number of bijective functions f:T→Tf : T\to T that satis es the following for all x∈Tx \in T: f(f(x))=xf(f(x)) = x ∣f(x)−x∣≥2|f(x) - x| \ge 2
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