Primes of the Form $x^2 + ny^2$ James A. Marley Professor of Special Education University

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Primes of the Form $x^2 + ny^2$ James A. Marley Professor of Special Education UniversityThis book studies when a prime $p$ can be written in the form $x^{2} + ny^{2}$. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class