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We announce a very general statement involving the rational quartic residuesymbol $(m/p)_4$ and, more generally, Legendre symbols of the type${a+b\sqrt{m}/p$. We show how our main theorem can be used to produce manyolder results such as Scholz's, Lehmer's or Burde's reciprocity laws and manyothers. It is very likely that all existing reciprocity laws of this type canbe obtained from our result. This is a corrected and improved version ofversion 2.

Reciprocity laws for Legendre symbols of the type $(a+b\sqrt{m}/p)$ - Long Version