Let $y$ be a natural number of 4 digits that is represented in the decimal system as $y = x_1x_2x_3x_4$. If $3|(x_1 + x_2 + x_3 + x_4)$ then $3|y$.
My attempt. What I did was suppose by contradiction that 3 $\nmid y = x_1x_2x_3x_4$. Then for every integer $k$, $x_1x_2x_3x_4 \neq 3k$. Particularly, putting $k=\frac{x_1+x_2+x_3+x_4}{3} \in \mathbb{Z}$, then $y=x_1x_2x_3x_4 \neq x_1+x_2+x_3+x_4$. From here, I am not sure what else to do to get an absurdity, since I already used the hypothesis. Any suggestion?