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[7] viXra:2006.0177 [pdf] submitted on 2020-06-18 14:15:01
Authors: Michael I. C. Nwogugu
Comments: 5 Pages.
In this article, its shown that the ABC Conjecture is correct for integers a+b=c, and any real number r>1. This article proposes that the ABC Conjecture is true iff: c>0.
Category: Algebra
[6] viXra:2006.0168 [pdf] submitted on 2020-06-18 14:05:16
Authors: Michael I. C. Nwogugu
Comments: 5 Pages.
In this article, its shown that the Miyazaki (2013) Conjecture is wrong and doesn’t apply to most Pythagoreans, (and that the Jesmanowicz Conjecture remains un-proven) within the context of Sub-Rings (ie. Integers).
Category: Algebra
[5] viXra:2006.0167 [pdf] submitted on 2020-06-18 14:06:21
Authors: Michael I. C. Nwogugu
Comments: 9 Pages.
The y-Increment Puzzle is a new phenomenon that is introduced herein, and occurs in exponential equations of the type x = rs-qs; in positive integers where r = (n+y1), q=(n-y2), and y1 and y2 may or may not be equal. This class of functions has wide applications in computer science, applied math, physics and finance/economics. Given the y-Increment Puzzle, the Law-of-Large-Numbers (LLN) isn’t valid for all time series.
Category: Algebra
[4] viXra:2006.0166 [pdf] submitted on 2020-06-18 14:07:40
Authors: Michael I. C. Nwogugu
Comments: 6 Pages.
The equation xa+yb+zc=m in real numbers is an ill-posed problem and can be used in physical sciences and social sciences. This article introduces some properties of xa+yb+zc=m in real numbers, and also defines “m-Stability”, a new measure of stability of nonlinear equations.
Category: Algebra
[3] viXra:2006.0165 [pdf] submitted on 2020-06-18 14:08:55
Authors: Michael I. C. Nwogugu
Comments: 11 Pages.
Some properties of the equations X2+Y2+Z2+V2=dXYZ, and X2+Y2+Z 2+V2+U2=dXYZ, and the Markoff Equation X2+Y2+Z2=aXYZ in real numbers are analyzed in this article, and common elements are highlighted, and the results are applicable where all variables are Integers (ie. proofs within the context of Sub-Rings).
Category: Algebra
[2] viXra:2006.0162 [pdf] submitted on 2020-06-18 14:14:01
Authors: Michael I. C. Nwogugu
Comments: 9 Pages.
This article introduces a second new proof of Fermat’s Last Conjecture (Nwogugu [2020] introduced the first new proof of Fermat’s Last Conjecture) which is studied in the context of Sub-Rings of Complex Numbers (Integers; Rationals).
Category: Algebra
[1] viXra:2006.0008 [pdf] replaced on 2020-07-01 01:59:06
Authors: George Plousos
Comments: 5 Pages. corrected
There is a characteristic form of nested radicals that contains many signs (+, -) and is expressed in a closed trigonometric form. When the value of the trigonometric expression is known, we are called to find the values of the signs of the radical representation (the reverse is easier). The solution is provided directly by the Gray code of an integer contained in the known member of this equation of signs. However, the method of converting integers to Gray code differs from the standard method and is easier. The reason is that I found the equivalent method without knowing the Gray code. At the same time, a model emerged that interprets and facilitates the conversion of a group of integers into Gray code.
Category: Algebra
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