Reducing radicals in the spirit of Euclid

2020/04/13 by Girstmair, Kurt
#12F10 #33F10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.06039

Abstract

Let p be an odd natural number ≥ 3. Inspired by results from Euclid's \em Elements, we express the irrational y=√[p]d+√ R, whose degree is 2p, as a polynomial function of irrationals of degrees ≤ 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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