Question 69
Let $N$ denote the set of positive integers. Find all functions $f : N \to N$ such that the equation
$$
\operatorname{lcm}(m, f(m + f(n))) = \operatorname{lcm}(f(m), f(m) + n)
$$
holds for any positive integers $m$ and $n$. Here, for positive integers $x$ and $y$, $\operatorname{lcm}(x, y)$ denotes their least common multiple.
$$
\operatorname{lcm}(m, f(m + f(n))) = \operatorname{lcm}(f(m), f(m) + n)
$$
holds for any positive integers $m$ and $n$. Here, for positive integers $x$ and $y$, $\operatorname{lcm}(x, y)$ denotes their least common multiple.