Question 34
Let $\mathbb{N}$ denote the set of all positive integers. Find all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that
$$
f(x + y(f(x))) = x + f(x)f(y)
$$
holds for all positive integers $x, y$.
$$
f(x + y(f(x))) = x + f(x)f(y)
$$
holds for all positive integers $x, y$.