论文标题
降低欧几里得精神的激进分子
Reducing radicals in the spirit of Euclid
论文作者
论文摘要
令$ p $是一个奇怪的天然数字$ \ ge 3 $。受Euclid的{\ em Elements}的结果的启发，我们表达了非理性$ y = \ sqrt [p] {d+\ sqrt r}，其度为$ 2p $的$ $，作为$ 2p $，是不理性的学位$ \ le p $的多样性。在某些情况下，$ y $由简单的激进分子表示。该度的降低表现出非常规定的多项式模式。该证明是基于Zeilberger算法的超几何概述。
Let $p$ be an odd natural number $\ge 3$. Inspired by results from Euclid's {\em Elements}, we express the irrational $$y=\sqrt[p]{d+\sqrt R}, $$ whose degree is $2p$, as a polynomial function of irrationals of degrees $\le p$. In certain cases $y$ is expressed by simple radicals. This reduction of the degree exhibits remarkably regular patterns of the polynomials involved. The proof is based on hypergeometric summation, in particular, on Zeilberger's algorithm.
