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KConrad
KConrad
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Imaginary quadratic fields: euclideanEuclidean if and only if norm euclideanEuclidean

Let $K$ be an imaginary quadratic field and $O_K$ be its ring of integers. I'llWe say $O_K$ is ring euclideannorm Euclidean if the norm is a euclideanEuclidean function. It is known from the classification of imaginary quadratic fields with class number 1 that $O_K$ is euclideanEuclidean if and only if it is norm euclideanEuclidean. Is there a more straightforward proof of this fact?

Imaginary quadratic fields: euclidean if and only if norm euclidean

Let $K$ be an imaginary quadratic field and $O_K$ be its ring of integers. I'll say $O_K$ is ring euclidean if the norm is a euclidean function. It is known from the classification of imaginary quadratic fields with class number 1 that $O_K$ is euclidean if and only if it is norm euclidean. Is there a more straightforward proof of this fact?

Imaginary quadratic fields: Euclidean if and only if norm Euclidean

Let $K$ be an imaginary quadratic field and $O_K$ be its ring of integers. We say $O_K$ is norm Euclidean if the norm is a Euclidean function. It is known from the classification of imaginary quadratic fields with class number 1 that $O_K$ is Euclidean if and only if it is norm Euclidean. Is there a more straightforward proof of this fact?

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George Shakan
George Shakan
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Imaginary quadratic fields: euclidean if and only if norm euclidean

Let $K$ be an imaginary quadratic field and $O_K$ be its ring of integers. I'll say $O_K$ is ring euclidean if the norm is a euclidean function. It is known from the classification of imaginary quadratic fields with class number 1 that $O_K$ is euclidean if and only if it is norm euclidean. Is there a more straightforward proof of this fact?