$$D(-1)$$ tuples in imaginary quadratic fields

• DOI: 10.1007/s10474-021-01150-w
• Publication Date: 2021-06-12T11:02:32Z
• Authors: S. Gupta
• Keywords: 0101 mathematics; 01 natural sciences

Let K be an imaginary quadratic number field, and $$ \mathcal{O}_K$$ its ring of integers. In this article, we prove the non-existence of Diophantine $$m$$ -tuples in $$\mathcal{O}_K$$ with the property $$D(-1)$$ , for $$m > 36$$ .