在欧几里得的精神中减少自由基
Reducing radicals in the spirit of Euclid
摘要：
令$p$为奇数自然数$\ge 3$。受Euclid的《\em元素》结果的启发，我们将次数为$2p$的无理数$$y=\sqrt[p]{d+\sqrt R}, $$表示为次数无理数$\le p$的多项式函数。在某些情况下，$y$用简单的部首表示。这种程度的减少表现出显着的规则模式的多项式。证明是基于超几何求和，特别是，在Zeilberger的算法。
英文摘要：
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.
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