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F:n----->n

Source: 17-th Iranian Mathematical Olympiad 1999/2000

December 14, 2005
functionfloor functionalgebra proposedalgebra

Problem Statement

Suppose f:N⟶Nf : \mathbb{N} \longrightarrow \mathbb{N} is a function that satisfies f(1)=1f(1) = 1 and f(n + 1) =\{\begin{array}{cc} f(n)+2&\mbox{if}\ n=f(f(n)-n+1),\\f(n)+1& \mbox{Otherwise}\end {array} (a)(a) Prove that f(f(n)−n+1)f(f(n)-n+1) is either nn or n+1n+1. (b)(b) Determineff.
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