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**idontknowanything** How can I show that the Hilbert Symbol is bimiltuplicative, when the local field is the p-adic numbers? Everything I can find just sort of asserts bimultiplicativity without much proof, so I'm guessing it's pretty straight forward, but I haven't done much work with the p-adics so I'm a little unclear.

Moreover, for what primes p is it the case that there exists an element z of the p-adics such that (-1, z) = -1. That is, the the Hilbert symbol acts on -1 and z and evaluates to -1.