MathDB

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

Problem Statement