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We discuss the origin, an improved definition and the key reciprocityproperty of the trilinear symbol introduced by R\'edei in the study of 8-ranksof narrow class groups of quadratic number fields. It can be used to show thatsuch 8-ranks are governed by Frobenius conditions on the primes dividing thediscriminant, a fact used the recent work of A. Smith. In addition, we explainits impact in the progress towards proving my conjectural density forsolvability of the negative Pell equation.

Redei reciprocity, governing fields, and negative Pell