ON THE REPRESENTATION OF PRIMES IN AS SUMS OF SQUARES
It is shown that the set of prime integers in is partitioned into two sets with respect to their representation as a sum of squares: (1) a set of primes that cannot be represented as a sum of squares; (2) a set 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 and use it to show how such representations in can be found with deterministic polynomial complexity.
Euclidean field, sum of squares, cyclotomic field, Euclidean Algorithm.