$x^y = y^{mx}$的正有理数解：一个数论探索
Positive rational solutions to $x^y = y^{mx}$: a number-theoretic excursion
摘要：
我们给一个轻松愉快的看看标题中的主题。大多数的解决方案是在半无聊的参数家庭，但有些是零星的，来自图厄方程。一个有趣的例子是m = 2，x =（4/5）^128，y =（4/5）^125。
英文摘要：
We give a light-hearted look at the topic in the title. Most solutions are in semi-boring parametric families, but some are sporadic and come from Thue equations. One amusing example is m = 2, x = (4/5)^128, y = (4/5)^125.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
