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f(f(n)) + f(n+1) = n+2; prove f(f(n)+n) = n+1

Source: 2012 Indonesia Round 2.5 TST 4 Problem 1

May 31, 2012
functioninductionfloor functionalgebra unsolvedalgebra

Problem Statement

Suppose a function f:Z+ā†’Z+f : \mathbb{Z}^+ \rightarrow \mathbb{Z}^+ satisfies f(f(n))+f(n+1)=n+2f(f(n)) + f(n+1) = n+2 for all positive integer nn. Prove that f(f(n)+n)=n+1f(f(n)+n) = n+1 for all positive integer nn.
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