Functions and Analysis

    

Existence Conditions, Asymptotic Behavior and Properties of a Class Of "Rational-Equivalence" Nonlinear Systems

Authors: Michael C. I. Nwogugu

Liptai, Németh, et. al. (2020) supposedly proved that in the diophantine equation (3^a−1)(3^b−1)=(5^c−1)(5^d−1) in positive integers and where a≤b and c≤d, the only solution to the title equation is (a,b,c,d)=(1,2,1,1). This article analyzes the Complexity of, and introduces properties of the equations (3^a−1)(3^b−1)=(5^c−1)(5^d−1) and g^u=f^v, new "Existence Conditions", new theories of "Rational Equivalence", and a new theorem pertaining to the equation g^u=f^v. The class of equations of the type [(X^a−1)(X^b−1)=(Y^c−1)(Y^d−1)] (the "Rational-Equivalence Equation") includes the equation (3^a−1)(3^b−1)=(5^c−1)(5^d−1). This article also introduces simple Java codes for finding solutions to this class of equations for positive-integers up to (10)^2457600000 (and even greater positive-integers depending on available computing power).

Comments: 10 Pages. The copyright license-type for this article is CC-BY-NC-ND.

Download: PDF

Submission history

[v1] 2022-08-09 00:43:00

Unique-IP document downloads: 209 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