BdMO TST Mock Exam 01 - 2021 - Problem 04 - Determine all surjective function such that the image is sum-free
Posted: Sat Jul 31, 2021 4:02 pm
Let $\mathbb{N}$ be the set of all positive integers. A subset $A$ of $\mathbb{N}$ is sum-free if, whenever $x$ and $y$ are (not necessarily distinct) elements of $A$, their sum $x+y$ does not belong to $A$. determine all surjective functions $f:\mathbb{N}\to\mathbb{N}$ such that, for each sum-free subset $A$ of $\mathbb{N}$, the image $\{f(a):a\in A\}$ is again sum-free.