MathNet 2011 Question 10

Let $f(x_1,\ldots,x_n)$ be an integer-coefficient polynomial of total degree less than $n$. Prove that the number of ordered tuples $(x_1,\ldots,x_n)$ with $0\le x_i\le12$ and
$$f(x_1,\ldots,x_n)\equiv0\pmod{13}$$
is divisible by13.