论文标题
在与卢卡斯序列的两个连续术语的幂有关的指数二约汀方程上
On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
论文作者
论文摘要
令$ r \ ge 1 $为整数，$ {\ bf u}：=（u_ {n}）_ {n \ ge 0} $是由$ u_0 = 0 $，$ u_1 = 1，$ u_1 = 1，$和$ u_ {n+2} = ru_ {n+1} ru_ {n+1}+n $ n $ n $ n $ n $ n $ n $ y $ lucas序列。在本文中，我们表明没有正整数$ r \ ge 3，〜x \ ne 2，〜n \ ge 1 $，因此$ u_n^x+u_ {n+1}^x $是$ {\ bf u} $的成员。
Let $r\ge 1$ be an integer and ${\bf U}:=(U_{n})_{n\ge 0} $ be the Lucas sequence given by $U_0=0$, $U_1=1, $ and $U_{n+2}=rU_{n+1}+U_n$, for all $ n\ge 0 $. In this paper, we show that there are no positive integers $r\ge 3,~x\ne 2,~n\ge 1$ such that $U_n^x+U_{n+1}^x$ is a member of ${\bf U}$.
