Question 128
Find all positive integers $k$, so that there exists a polynomial $f(x)$ with rational coefficients, such that for all sufficiently large $n$,
$$
f(n) = \operatorname{lcm}(n + 1, n + 2, \dots, n + k).
$$
$$
f(n) = \operatorname{lcm}(n + 1, n + 2, \dots, n + k).
$$