Determine the $(a, b)$ natural integers greater than or equal to 3 such that: $a b^{2}+b+7 \mid a^{2} b+a+b$
$$
\begin{gathered}
a b^{2}+b+7 \mid a^{2} b+a+b \\
a b^{2}+b+7 \mid a^{2} b^{2}+a b+b^{2} \\
a b^{2}+b+7 \mid a^{2} b^{2}+a b+7 a \\
a b^{2}+b+7 \mid b^{2}-7 a
\end{gathered}
$$

Or $b^{2}-7 a=0$, $f(x+f(x)+y)=f(y)+2 x$.

Exercise $3$ $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $\forall x, y \in \mathbb{R}, f(f(x)-x f(y))+x y=2 f(x)$.