ÖMO 2014 Problem 4

For an integer $n$ let $M (n) = \{n, n + 1, n + 2, n + 3, n + 4\}$ . Furthermore, be $S (n)$ sum of squares and $P (n)$ the product of the squares of the elements of $M (n)$ . For which integers $n$ is $S (n)$ a divisor of $P (n)$ ?