Problem

Source: MEMO 2015, problem I-1

Tags: function, algebra



Find all surjective functions f:NN such that for all positive integers a and b, exactly one of the following equations is true: f(a)=f(b),f(a+b)=min 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.