Representing Primes as the Form $x^2+n{y}^2$ in Some Imaginary Quadratic Fields

Abstract

We give criteria of the solvability of the diophantine equation $p=x^2+n{y}^2$ over some imaginary quadratic fields where $p$ is a prime element. The criteria becomes quite simple in special cases.

8 pages, This paper has been withdrawn by the author since it was merged into the article arXiv:1405.5776 on August 8, 2014