Question 188
Let $p$ be a prime number and $A$ be an infinite subset of natural numbers. Let $f_{A}(n)$ be the number of solutions other than $x_{1}+x_{2}+\cdots+x_{p}=n$ equation, with $x_{1}, x_{2}, \ldots, x_{p} \in A$. Is there any natural number $N$ such that $f_{A}(n)$ is constant for all $n\gt N$ ?