Representing multiples of m in real quadratic fields as sums of squares

Abstrakt

We study real quadratic fields Q(D--SQUARE ROOT) such that, for a given rational integer m, all m-multiples of totally positive integers are sums of squares. We prove quite sharp necessary and sufficient conditions for this to happen.

Further, we give a fast algorithm that solves this question for specific m, D and we give complete results for m<=5000.

Klíčová slova

• multiples
• real quadratic fields
• sums
• squares