Consider the monic polynomial $$f: = X^n + a_1 X^{n-1} + \cdots + a_n$$ over $\mathbb Z$. Let $p_i$ be the $i$_th power sum ($1 \le i \le n$) of the roots of $f$ (in some extension of $\mathbb Z$). What is the formula for ${a_1}^2 + {a_2}^2 + \cdots + {a_n}^2$ in terms of the $p_i$ ($1 \le i \le n$).
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