Question 4
Let $\mathbb{R}_+$ be the set of all positive integers. Find all functions $g: \mathbb{R}_+ \to \mathbb{R}_+$ such that numbers $x, y \in \mathbb{R}_+$ satisfy the equality
$$
xg(x + g(y)) = g(g(xy) + 1).
$$
$$
xg(x + g(y)) = g(g(xy) + 1).
$$