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arxiv: 1405.7109 · v2 · pith:WY73DACInew · submitted 2014-05-28 · 🧮 math.NT

Representing Primes as the Form x²+ny² in Some Imaginary Quadratic Fields

classification 🧮 math.NT
keywords criteriafieldsimaginaryquadraticsomebecomescasesdiophantine
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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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