论文标题
等式的分辨率$（3^{x_1} -1）（3^{x_2} -1）=（5^{y_1} -1）（5^{y_2} -1）$
Resolution of the equation $(3^{x_1}-1)(3^{x_2}-1)=(5^{y_1}-1)(5^{y_2}-1)$
论文作者
论文摘要
请考虑二聚体方程$（3^{x_1} -1）（3^{x_2} -1）=（5^{y_1} -1）（5^{y_2} -1）$ in积极整数中的$方程的每一侧分别是给定二进制复发的两个术语的产物。在本文中，我们证明标题方程的唯一解决方案是$（x_1，x_2，y_1，y_2）=（1,2,1,1）$。结果的主要新颖性是，我们允许双方两个术语。
Consider the diophantine equation $(3^{x_1}-1)(3^{x_2}-1)=(5^{y_1}-1)(5^{y_2}-1)$ in positive integers $x_1\le x_2$, and $y_1\le y_2$. Each side of the equation is a product of two terms of a given binary recurrence, respectively. In this paper, we prove that the only solution to the title equation is $(x_1,x_2,y_1,y_2)=(1,2,1,1)$. The main novelty of our result is that we allow products of two terms on both sides.
