Đề tài " The Hopf condition for bilinear forms over arbitrary fields "

We settle an old question about the existence of certain ‘sums-of-squares’ formulas over a field F , related to the composition problem for quadratic forms. A classical theorem says that if such a formula exists over a field of characteristic 0, then certain binomial coefficients must vanish. We prove that this result also holds over fields of characteristic p

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