论文标题
关于Diophantine方程的解决方案$ l_n+l_m = 3^a $
On solutions of the Diophantine equation $L_n+L_m=3^a$
论文作者
论文摘要
令$（l_n）_ {n \ geq 0} $为$ l_0 = 2，l_1 = 1 $和$ l_ {n+2} = l_ {n+1}+l_n $ for $ n \ geq 0 $。在本文中，我们有兴趣找到三个卢卡斯号的总和，即，我们研究指数型双苯胺方程$ l_n + l_m = 3^{a} $在非负整数$ n，m，m，$和$ a $中。我们的主要定理的证明使用对数中线性形式的下限，持续分数的属性以及在二磷酸近似中的Baker-Davenport减少方法的版本。
Let $(L_n)_{n\geq 0}$ be the Lucas sequence given by $L_0 = 2, L_1 = 1$ and $L_{n+2} = L_{n+1}+L_n$ for $n \geq 0$. In this paper, we are interested in finding all powers of three which are sums of two Lucas numbers, i.e., we study the exponential Diophantine equation $L_n + L_m = 3^{a}$ in nonnegative integers $n, m,$ and $a$. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.
