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Let $K$ be a field with non-zero elements $a,b,c \in K$ and let $(. , .)$ be the Hilbert symbol.

Let $(a,-c)=(-1,ac)$ and $(b,-c)=(-1,bc)$.

How to show that $(-ab,-c)=(-1,-abc)$ ?

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    Thanks! It's clear now :-)2012-12-02

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