Number Theory

    

Sixth Degree Diophantine Polynomial Equation

Authors: Oliver Couto

Historicaly, we note that finding a prametrization of degree six has not been easy. In the below paper the author has followed in the footsteps of below mentioned paper, ref. no. (1). In ref. no.(1), Ajai Choudhry on page 356 has parametrized equation: m(abc)(ab+bc+ca)(a+b+c)=n(pqr)(pq+pr+qr)(p+q+r), where, (m,n)=(3,32) using one parameter. In the below paper the author has parametrized the said equation for (m,n)=(1,1), but with two parameters. The trick used is to split equation (1) into three parts, so as to balance the coefficents (m,n) & such that, (m,n)=[(uvw),(xyz)]. And [(uvw),(xyz)] =(72,72), & hence they cancel each other out.

Comments: 5 Pages.

Download: PDF

Submission history

[v1] 2024-08-05 21:05:43

Unique-IP document downloads: 147 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus