NL-BXMO-TST 2010 Problem 5

For any non-negative integer $n$ , we say that a permutation $(a_0,a_1,...,a_n)$ of $\{0,1,..., n\}$ is quadratic if $k + a_k$ is a square for $k = 0, 1,...,n$ . Show that for any non-negative integer $n$ , there exists a quadratic permutation of $\{0,1,..., n\}$ .