Representing Primes as the Form $x^2+ny^2$ in Some Imaginary Quadratic Fields

preprint2015arXivOpen access

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

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Representing Primes as the Form $x^2+ny^2$ in Some Imaginary Quadratic Fields

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Representing Primes as the Form x2+ny2x^2+ny^2x2+ny2 in Some Imaginary Quadratic Fields

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Representing Primes as the Form $x^2+ny^2$ in Some Imaginary Quadratic Fields