The aim of this chapter is to present those proofs of the quadratic reciprocity law which are based on the theory of quadratic number fields. The first proof using such techniques was Gauss’s second proof; instead of developing the theory of binary quadratic forms we will give a proof using the ideal theoretic language. After developing the complete genus theory for quadratic number fields, we give some applications to the primality tests of Lucas-Lehmer.
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- Quadratic Number Fields
- Springer Berlin Heidelberg