Question 77
Let non-constant polynomial $f(x)$ with real coefficients is given with the following property: for any positive integer $n$ and $k$, the value of expression
$$
\frac{f(n+1) f(n+2) \ldots f(n+k)}{f(1) f(2) \ldots f(k)} \in \mathbb{Z} .
$$
Prove that $f(x)$ is divisible by $x$.
$$
\frac{f(n+1) f(n+2) \ldots f(n+k)}{f(1) f(2) \ldots f(k)} \in \mathbb{Z} .
$$
Prove that $f(x)$ is divisible by $x$.