Methods for arriving at numerical solutions for equations of the type [k+3] and [k+5] biquadratics equal to a bi-quadratic for different values of k

Seiji Tomita; Oliver Couto

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arXiv · 2206.01277

Methods for arriving at numerical solutions for equations of the type [k+3] and [k+5] biquadratics equal to a bi-quadratic for different values of k

Seiji Tomita·Oliver Couto

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Abstract

Different authors have done analysis regarding sums of powers References number 1,2 and 3, but systematic approach for solving Diophantine equations having sums of many biquadratics equal to a quartic has not been done before. In this paper we give methods for finding numerical solutions to equation A given above in section one. Next in section two, we give methods for finding numerical solutions for equation B given above. As is known that finding parametric solutions to biquadratic equations is not easy by conventional method. So the authors have found numerical solutions to equation A and B using elliptic curve theory.

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Seiji Tomita, Oliver Couto. 2022-05-13. Methods for arriving at numerical solutions for equations of the type [k+3] and [k+5] biquadratics equal to a bi-quadratic for different values of k. https://arxiv.org/abs/2206.01277

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