Harbingers of Artin's Reciprocity Law. I. The Continuing Story of Auxiliary Primes
11A15, 11R37 | Mathematics - Number Theory | Mathematics - History and Overview
In this article we present the history of auxiliary primes used in proofs of reciprocity laws from the quadratic to Artin's reciprocity law. We also show that the gap in Legendre's proof can be closed with a simple application of Gauss's genus theory.