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