I am looking for the reference to Hasse's original publication classifying the Quaternion algebras over a number field $K$. The statement in the paper or book should read something like:
``Two Quaternion algebras over a number field $K$ are isomorphic iff they are ramified at the same number of places"
As detailed here, Hasse introduced an invariant, now known as the Hasse invariant in two papers (here and here) to classify central simple algebras.