论文标题
Jacobi符号标准涉及$ K $ -FIBONACCI和$ K $ -LUCAS数字和椭圆曲线上的整数点
A Jacobi Symbol Criterion Involving $k$-Fibonacci and $k$-Lucas numbers and Integer Points on Elliptic Curves
论文作者
论文摘要
1989年，Ming Luo \ cite {l2}表明，fibonacci $ u_n $是三角形的，并且仅当$ n = \ pm1,2,4,8,10 $。为此，他建立了雅各比符号标准。此外，他观察到这个问题等于在两个椭圆曲线上找到所有整数点。在本文中，我们证明了雅各比的符号标准，用于更多的二元复发家庭。此外，应用标准和基本方法，我们确定椭圆曲线上的所有整数点$ y^2 = 5x^2（x+3）^2+4（-1）^n $。
In 1989, Ming Luo \cite{L2} showed that the Fibonacci number $U_n$ is Triangular if and only if $n=\pm1,2,4,8,10$. For this, he established a Jacobi Symbol Criterion. Moreover, he observed that this problem is equivalent to finding all integer points on two elliptic curves. In this paper, we prove a Jacobi Symbol Criterion for more general families of binary recurrences. In addition, applying the criterion and elementary methods, we determine all integer points on the elliptic curves $y^2=5x^2(x+3)^2+4(-1)^n$.
