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Consider the quadratic field ... and the associated ring of integers ... , where ... if ... and ... if ... . We assume ... is principal but not necessarily Euclidean. We compute the GCD of two elements ... , ... of ... modulo a unit of ... . The computation also gives explicit coefficients ... , ... for the Bézout identity ... . This is done by reducing binary quadratic forms and considering the sum of ideals ... as the ideal ... , with ... .

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      EUN,LOM,LRE4,work-cmr-id:398409,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/ExtendedGCDOfQuadraticIntegers/,ilox,learning resource exchange,LRE metadata application profile,LRE

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