标题： 立方数周围不存在连续的强三元组，这些立方数具有素数平方因子 显示英文标题

标题： Nonexistence of Consecutive Powerful Triplets Around Cubes with Prime-Square Factors

摘要： 埃尔德什-莫林-沃尔什猜想，断言不存在三个连续的强整数，仍然是数论中一个著名的未解问题。 一条自然的研究方向，继陈（2025）最近的工作之后，是研究围绕完美立方体的潜在反例，这些立方体本身也是强整数。 本文建立了一个关于具有不同结构约束的此类整数三元组的新非存在性结果，结合了模算术、$p$-adic 估值以及椭圆曲线理论的技术。 显示英文摘要

摘要： The Erd\H{o}s-Mollin-Walsh conjecture, asserting the nonexistence of three consecutive powerful integers, remains a celebrated open problem in number theory. A natural line of inquiry, following recent work by Chan (2025), is to investigate potential counterexamples centered around perfect cubes, which are themselves powerful. This paper establishes a new non-existence result for a family of such integer triplets with distinct structural constraints, combining techniques from modular arithmetic, $p$-adic valuation, and the theory of elliptic curves.