  For any given set $A$ of nonnegative integers and for any given two positive
integers $k_1,k_2$, $R_{k_1,k_2}(A,n)$ is defined as the number of solutions of
the equation $n=k_1a_1+k_2a_2$ with $a_1,a_2\in A$. In this paper, we prove
that if integer $k\geq2$ and set $A\subseteq\mathbb{N}$ such that
$R_{1,k}(A,n)=R_{1,k}(\mathbb{N}\setminus A,n)$ holds for all integers $n\geq
n_0$, then $R_{1,k}(A,n)\gg \log n$.
