Diophantine equation of degree sixteen

Oliver Couto; Seiji Tomita

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arXiv · 2211.00440

Diophantine equation of degree sixteen

Oliver Couto·Seiji Tomita

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Abstract

While there is not much publications, about degree sixteen Diophantine equation we do have an identity given by Ramanujan (ref. #1). Also on the internet even though there are numerical solutions to degree sixteen for eg. (16-7-24) equation (ref. #5) there are hardly any parametric solutions. An Octic degree parameterization has been arrived at by Choudhry & Zagar (ref. 2). The authors have given a parametric solution to the equation (a^4-b^4)(c^4-d^4)(e^8-f^8)=(u^4-v^4)(w^4-x^4)(y^8-z^8). We have also given numerical solution but because of the high degree (sixteen) of the equation we only get a minimum integer value for the variables at more than five digits. We have also given some new identities related to degree four & eight.

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BibTeX RIS

Oliver Couto, Seiji Tomita. 2022-10-11. Diophantine equation of degree sixteen. https://arxiv.org/abs/2211.00440

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