3-variable Linear Forms With Unique Representation Of Every Integer

Let a,b,and c be distinct positive integers,this paper mainly studies whether there is a set A ? Z,such that for every integer n,it can be represented uniquely as n = ax + by + cz,where x,y,z ∈ A,we get the necessary and sufficient condition for the existence of set A.This paper comes from a question posed by Nathanson,in this paper,we solve the case of the function of three variables,and we also make a certain discussion of the case of the function of multiple variables.