On the Representation of Primes in Q(2^(1/2) as Sums of Squares
Michele Elia, Chris Monico · PORTO Publications Open Repository TOrino (Politecnico di Torino) · 2007
It is shown that the set of prime integers in Q( √ 2) is partitioned into two sets with respect to their representation as a sum of squares: 1) a set S0 of primes that cannot be represented as a sum of squares; 2) a set S2 of primes that can be represented as a sum of two squares. Moreover, we give an effective, polynomial-time Euclidean Algorithm for the ring of integers of the cyclotomic field Q(ζ8) and use it to show how such representations in Q( √ 2) can be found with deterministic polynomial complexity.