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

Martin Raška

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arXiv · 2105.11423

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

Martin Raška

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Abstract

We study real quadratic fields $\mathbb{Q}(\sqrt{D})$ 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 $m \leq 5000$.

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BibTeX RIS

Martin Raška. 2021-05-24. Representing multiples of $m$ in real quadratic fields as sums of squares. https://arxiv.org/abs/2105.11423

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