论文标题
偶发的二芬太丁四肢
Doubly regular Diophantine quadruples
论文作者
论文摘要
For a nonzero 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 1 <= i < j <= m, is called a D(n)-m-tuple.在本文中，通过使用所谓的常规双苯胺m-tuples和某些椭圆曲线系列的属性，我们表明，有许多本质上不同的集合，由完美的正方形组成，这些平方同时d（n_1）-quadruples和d（n_2） - Quadruples和d（n_2） - Quadruplace，具有不同的非非区域n_1和n_1和n_1和n_1和n__2。
For a nonzero 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 1 <= i < j <= m, is called a D(n)-m-tuple. In this paper, by using properties of so-called regular Diophantine m-tuples and certain family of elliptic curves, we show that there are infinitely many essentially different sets consisting of perfect squares which are simultaneously D(n_1)-quadruples and D(n_2)-quadruples with distinct non-zero squares n_1 and n_2.
