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 $(-ab,-c)=(-1,-abc)$ ?
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 $(-ab,-c)=(-1,-abc)$ ?