MEMO 2015 I1

Find all surjective functions $f:\mathbb{N}\to\mathbb{N}$ such that for all positive integers $a$ and $b$ , exactly one of the following equations is true: \begin{align*} f(a)&=f(b), f(a+b)&=\min{f(a),f(b)}. \end{align*} Remarks: $\mathbb{N}$ denotes the set of all positive integers. A function $f:X\to Y$ is said to be surjective if for every $y\in Y$ there exists $x\in X$ such that $f(x)=y$ .