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Prove that f(n+f(n))=n for each n - [Bulgaria NMO 2010]

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December 28, 2010
functionfloor functioninductionalgebra proposedalgebra

Problem Statement

Let f:Nā†’Nf: \mathbb N \to \mathbb N be a function such that f(1)=1f(1)=1 and f(n)=n - f(f(n-1)),   \forall n \geq 2. Prove that f(n+f(n))=nf(n+f(n))=n for each positive integer n.n.
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