Sums of squares of integer-multiple of an integral element on real bi-quadratic fields

Srijonee Shabnam Chaudhury

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arXiv · 2112.14489

Sums of squares of integer-multiple of an integral element on real bi-quadratic fields

Srijonee Shabnam Chaudhury

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Abstract

For any given positive integer $m$ we construct certain totally positive algebraic integers $\alpha$ of a real bi-quadratic field $K$ and obtain some necessary conditions for which $m\alpha$ can not be represented as sum of integral squares. We show this for integers lie in quadratic subfields of $K$ and for integers which are in $K$ but not in any quadratic subfield of $K$. We provide examples in tabular form for each cases to corroborate the results.

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BibTeX RIS

Srijonee Shabnam Chaudhury. 2021-12-29. Sums of squares of integer-multiple of an integral element on real bi-quadratic fields. https://arxiv.org/abs/2112.14489

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