论文标题
Abel-Ruffini的定理：复杂但不复杂！
Abel-Ruffini's Theorem: Complex but Not Complicated!
论文作者
论文摘要
在本文中，我们仅使用对复数的基本知识来勾勒出著名的亚伯 - 鲁夫尼定理的证明，该证明说，使用激进分子无法编写五级或多个代数方程式的一般解决方案，即使用其系数和其系数和arithmetic operations $+，$+， - ， - ， - ，$，$，$，$，$，$和$ \ sqrt =本文有目的地用简洁和教学的术语编写，并致力于不熟悉Galois理论的学生和研究人员，甚至是一般的群体理论，这是证明这一出色定理的常用工具。特别是，证据是独立的，并有一些见识，即为什么要对四个或更少的程度的公式（以及如何构造）以及为什么它们不占五个或更多。
In this article, using only elementary knowledge of complex numbers, we sketch a proof of the celebrated Abel--Ruffini theorem, which states that the general solution to an algebraic equation of degree five or more cannot be written using radicals, that is, using its coefficients and arithmetic operations $+,-,\times,÷,$ and $\sqrt{\ }$. The present article is written purposely with concise and pedagogical terms and dedicated to students and researchers not familiar with Galois theory, or even group theory in general, which are the usual tools used to prove this remarkable theorem. In particular, the proof is self-contained and gives some insight as to why formulae exist for equations of degree four or less (and how they are constructed), and why they do not for degree five or more.
