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For $m\geq 1$, let $0<b_0<b_1<...<b_m$ and $\ e_0,e_1,...,e_m>0$ be fixedpositive integers. Assume there exists a prime $p$ and an integer $t>0$ suchthat $p^t\mid b_0$, but $p^t\nmid b_{i}\ {\rm for}\ 1\leq i\leq m$.  Then, we prove that there is no infinite subset $\mathcal A$ of positiveintegers, such that the number of solutions of the following equation$$n=b_0(a_{0,1}+...+a_{0,e_0})+...+b_m(a_{m,1}+...+a_{m,r_m}),\ a_{i,j}\in\mathcal A$$ is constant for $n$ large enough. This result generalizes therecent result of Cilleruelo and Ru\'{e} for bilinear case, and answers aquestion posed by S\'{a}rkozy and S\'{o}s.

A question of S\'{a}rkozy and S\'{o}s on representation functions] {A question of S\'{a}rkozy and S\'{o}s on representation functions