On natural numbers having unique factorization in a quadratic number field
نویسندگان
چکیده
منابع مشابه
A New GCD Algorithm for Quadratic Number Rings with Unique Factorization
We present an algorithm to compute a greatest common divisor of two integers in a quadratic number ring that is a unique factorization domain. The algorithm uses O(n log n log log n + ∆ 1 2 + ) bit operations in a ring of discriminant ∆. This appears to be the first gcd algorithm of complexity o(n) for any fixed non-Euclidean number ring. The main idea behind the algorithm is a well known relat...
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Following what is basically Kummer’s relatively neglected approach to non-unique factorization, we determine the structure of the irreducible factorizations of an element n in the ring of integers of a number field K. Consequently, we give a combinatorial expression for the number of irreducible factorizations of n in the ring. When K is quadratic, we show in certain cases how quadratic forms c...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1966
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-12-1-1-22