There is no Diophantine D(−1)$D(-1)$‐quadruple

نویسندگان

چکیده

A set of positive integers with the property that product any two them is successor a perfect square called Diophantine D ( − 1 ) $D(-1)$ -set. Such objects are usually studied via system generalized Pell equations naturally attached to under scrutiny. In this paper, an innovative technique introduced in study -quadruples. The main novelty uncovering quadratic equation relating various parameters describing hypothetical -quadruple integer entries. combination extensive computations, idea leads confirmation conjecture according which there no

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ژورنال

عنوان ژورنال: Journal of the London Mathematical Society

سال: 2022

ISSN: ['1469-7750', '0024-6107']

DOI: https://doi.org/10.1112/jlms.12507