Question 6
(GER 1; IMO 5) Let $\mathbb N=\{1,2,3,\ldots\}$. Determine whether there exists a strictly increasing function $f:\mathbb N\to\mathbb N$ with the following properties:
$$f(1)=2;\tag{1}$$
$$f(f(n))=f(n)+n\qquad(n\in\mathbb N).\tag{2}$$
$$f(1)=2;\tag{1}$$
$$f(f(n))=f(n)+n\qquad(n\in\mathbb N).\tag{2}$$