lean_workbook_plus_64142

Let $d$ be a positive integer. Show that for every integer $S$ , there exists an integer $n>0$ and a sequence of $n$ integers $\epsilon_1, \epsilon_2,..., \epsilon_n$ , where $\epsilon_i = \pm 1$ (not necessarily dependent on each other) for all integers $1\le i\le n$ , such that $S=\sum_{i=1}^{n}{\epsilon_i(1+id)^2}$ .