论文标题
没有Diophantine $ d（-1）$ - 四倍体
There is no Diophantine $D(-1)$--quadruple
论文作者
论文摘要
一组带有属性的积极整数是其中任何两个的产物都是完美广场的后继产品，称为Diophantine $ d（-1）$ - set。通常，通过自然连接到审查的集合的广义pelt方程系统来研究此类物体。在本文中，在Diophantine $ d（-1）$ - 四倍体的研究中引入了一种创新技术。主要的新颖性是揭露一个二次方程，该方程将各种参数描述了一个假设的$ d（-1）$ - 四倍 - 与整数条目相关。结合广泛的计算结合使用，此想法可导致对猜想的确认，根据该猜想，没有Diophantine $ d（-1）$ - 四倍。
A set of positive integers with the property that the product of any two of them is the successor of a perfect square is called Diophantine $D(-1)$--set. Such objects are usually studied via a system of generalized Pell equations naturally attached to the set under scrutiny. In this paper, an innovative technique is introduced in the study of Diophantine $D(-1)$--quadruples. The main novelty is the uncovering of a quadratic equation relating various parameters describing a hypothetical $D(-1)$--quadruple with integer entries. In combination with extensive computations, this idea leads to the confirmation of the conjecture according to which there is no Diophantine $D(-1)$--quadruple.
