Problem

Source: 2012 Indonesia Round 2.5 TST 4 Problem 1

Tags: function, induction, floor function, algebra unsolved, algebra



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