Reducing radicals in the spirit of Euclid. (May 2021) - Girstmair, Kurt
Abstract: Let p be an odd natural number ≥3. Inspired by results from Euclid's Elements, we express the irrational y = d + R p, whose degree is 2 p, 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.