Gauss, Eisenstein, and the ``third'' proof of the quadratic reciprocity theorem: Ein kleines Schauspiel (Q1345071)

The authors compare Gauss and Eisenstein, in a prescient dialogue, their arguments for the quadratic reciprocity law. With \(p\) and \(q\) the odd primes, Gauss begins by multiplying \(q\) by the \(p\)-residues less than \(p/2\) while Eisenstein uses the even \(p\)-residues. The reader is led to a new appreciation of Eisenstein's insight.