Spring 2017, problem 46
Let $f: \mathbb N \to \mathbb N$ be a function such that $f(1)=1$ and $$f(n)=n - f(f(n-1)), \quad n \geq 2.$$ Show that $f(n+f(n))=n $ for each positive integer $n.$
Let $f: \mathbb N \to \mathbb N$ be a function such that $f(1)=1$ and $$f(n)=n - f(f(n-1)), \quad n \geq 2.$$ Show that $f(n+f(n))=n $ for each positive integer $n.$