MathDB

4

Part of 2020 Romanian Master of Mathematics

Problems(1)

Function preserves sum-free-ness

Source: Romanian Masters of Mathematics 2020, Problem 4

3/1/2020
Let N\mathbb N be the set of all positive integers. A subset AA of N\mathbb N is sum-free if, whenever xx and yy are (not necessarily distinct) members of AA, their sum x+yx+y does not belong to AA. Determine all surjective functions f:N→Nf:\mathbb N\to\mathbb N such that, for each sum-free subset AA of N\mathbb N, the image {f(a):a∈A}\{f(a):a\in A\} is also sum-free.
Note: a function f:N→Nf:\mathbb N\to\mathbb N is surjective if, for every positive integer nn, there exists a positive integer mm such that f(m)=nf(m)=n.
functionalgebraRMMRMM 2020