论文标题
D（n） - 具有正方形元素的Quintuples
D(n)-quintuples with square elements
论文作者
论文摘要
对于整数n，一组不同的非零整数{a_1，a_2，...，a_m}，使得a_i a_j+n是所有0 <i <i <j <m+1的理想之选，称为a d（n）-m-m-tuple。在本文中，我们表明有许多基本不同的D（n）Quintuples具有正方形的元素。我们通过在沿着四个曲线分支的A^2的一定双盖上构造一属属，从而获得了这一结果。
For an integer n, a set of m distinct nonzero integers {a_1,a_2,...,a_m} such that a_i a_j+n is a perfect square for all 0<i<j<m+1, is called a D(n)-m-tuple. In this paper, we show that there are infinitely many essentially different D(n)-quintuples with square elements. We obtained this result by constructing genus one curves on a certain double cover of A^2 branched along four curves.
