... (n,n2).Proof. The proof is by induction. The result for Q0is obvious, and the result for Q1∼=P1is Property (D).Except for the base cases in the previous paragraph, the argument for the odd and ... [A2] and Yuzvinsky [Y] for special values of r, s, and n. In [SS]a weaker version of the condition was proved for arbitrary fields and arbitraryvalues of r, s, and n.Stiefel’s proof of the condition ... an+1= 0 and ai= 0 fori ≤ n.Proof. The claims are immediate from the calculation since all the powers of τ are nonzero.Proof of Theorem 1.2. Suppose we have a sums -of- squares formula of type[r,...