TW-TST 2001 Problem 5

Let $f(n)=\sum_{k=0}^{n-1}x^ky^{n-1-k}$ with, $x$ , $y$ real numbers. If $f(n)$ , $f(n+1)$ , $f(n+2)$ , $f(n+3)$ , are integers for some $n$ , prove $f(n)$ is integer for all $n$ .