Let $a_0$ and $b_0$ be smooth compactly supported functions in $\Omega \subset R^3$, $f\in C^1(\Omega)$ and define

$a_n=f\Delta^{-1}(a_{n-1})=-f(x)\int_{\Omega}a_{n-1}(y)\Phi(x-y)dy$, $n\geq 1$

$b_n=f\Delta^{-1}(b_{n-1})=-f(x)\int_{\Omega}b_{n-1}(y)\Phi(x-y)dy$, $n\geq 1$

where $\Phi$ is the fundamental solution of the laplacian. Suppose

$\int_{\Omega}(a_n-b_n)\varphi=0$ for every harmonic function $\varphi$ and every $n\geq 0$. Is $a_0=b_0$?