Archivio Istituzionale della RicercaIn the quadratic number field with the golden section unit, any prime p has associated primes that are the sums of two integer squares, if and only if its field norm N(p) is not a rational prime congruent to 11 or 19 modulo 20. A proof of this property is presented, along with a method for computing the two squares with deterministic polynomial complexity, that is, using a number of arithmetical operations proportional to a power of log2 N(p) of bounded exponent.
Representation of Primes as the Sums of Two Squares in the Golden Section Quadratic Field / Elia, Michele. - In: JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY. - ISSN 0972-0529. - STAMPA. - 9:(2006), pp. 25-37.
Representation of Primes as the Sums of Two Squares in the Golden Section Quadratic Field
ELIA, Michele
2006
Abstract
In the quadratic number field with the golden section unit, any prime p has associated primes that are the sums of two integer squares, if and only if its field norm N(p) is not a rational prime congruent to 11 or 19 modulo 20. A proof of this property is presented, along with a method for computing the two squares with deterministic polynomial complexity, that is, using a number of arithmetical operations proportional to a power of log2 N(p) of bounded exponent.
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https://hdl.handle.net/11583/1401672
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