Question 75
Determine all positive integers $n$ for which there exists a polynomial $f(x)$ with real coefficients, with the following properties:
1) for each integer $k$, the number $f(k)$ is an integer if and only if $n$ does not divide $k$;
2) the degree of $f$ is less than $n$.
1) for each integer $k$, the number $f(k)$ is an integer if and only if $n$ does not divide $k$;
2) the degree of $f$ is less than $n$.