Mathematical Framework and Computational Results Associated with Rational Points on Fermat’s Surfaces in Minkowski’s (N+1) - Dimensional Spaces and Extended Fermat’s Last Theorem | Chapter 10 | Research Updates in Mathematics and Computer Science Vol. 7

 

 

Despite the elaborate Wiles demonstration, Fermat’s last theorem still attracts researchers to this aspect of number theory. This study has been structured in two parts. The first one describes the Minkowski natural space basis, where the discussion of Fermat’s theorem and the extensions to higher dimensional spacesss. In the second, many examples of N-dimensional vectors obeying a Fermat-like rule for various powers are presented and discussed. The Fermat last theorem, defined in (2+1)-dimensional Minkowski spaces, is discussed and extended in natural and rational Mikowski’s spaces. Several pieces of computational interest are given, with many practical examples. A definition of Fermat vector order, Fermat surfaces, and Fermat surface radius is given. Several conjectures are discussed, among them the existence of a Fermat theorem in (3+1)-dimensional Minkowski spaces.

 

Author(s) Details

Ramon Carbó-Dorca

Institut de Química Computacional, Universitat de Girona, Girona 17005 (Catalonia), Spain and Ronin Institute, 127 Haddon Place, Montclair N. J. 07043, USA.

 

Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v7/1756G

 

Mathematical Framework and Computational Results Associated with Rational Points on Fermat’s Surfaces in Minkowski’s (N+1) - Dimensional Spaces and Extended Fermat’s Last Theorem | Chapter 11 | Research Updates in Mathematics and Computer Science Vol. 7

 

Despite the elaborate Wiles demonstration, Fermat’s last theorem still attracts researchers to this aspect of number theory. This study has been structured in two parts. The first one describes the Minkowski natural space basis, where the discussion of Fermat’s theorem and the extensions to higher dimensional spacesss. In the second, many examples of N-dimensional vectors obeying a Fermat-like rule for various powers are presented and discussed. The Fermat last theorem, defined in (2+1)-dimensional Minkowski spaces, is discussed and extended in natural and rational Mikowski’s spaces. Several pieces of computational interest are given, with many practical examples. A definition of Fermat vector order, Fermat surfaces, and Fermat surface radius is given. Several conjectures are discussed, among them the existence of a Fermat theorem in (3+1)-dimensional Minkowski spaces.

 

Author(s)details:-

 

Ramon Carbó-Dorca
Institut de Química Computacional, Universitat de Girona, Girona 17005 (Catalonia), Spain and Ronin Institute, 127 Haddon Place, Montclair N. J. 07043, USA.

 

Please See the book here :- https://doi.org/10.9734/bpi/rumcs/v7/1756G

Godelian Encryption and Goldbach’s Conjecture | Chapter 6 | New Trends in Physical Science Research Vol. 8

 

This document describes an idea for an unbreakable encryption and decryption technology within its difference  quotient from (an) appropriate methodology  and arranged in modular relationships. Based on a Gödel vacuum concept, the dependency of the Goldbach conjecture is a proposition for which preliminary proof is granted or not within the vacuum mathematical structure of retractable or reductive proofs, in favor of the stochastic of   pretext of a multitude of homological errors and congruences. The co-terminal relation of two modular relations  in  power to establish the advantages of  the algebraic exponential exponential fundamental theorem, the reduction of an information capacity requirement to leverage the pretense of decreasing computational algebraic and geometric  exponents (rays) (true) logarithmic compressibility in a conventional binary machine. What seems "distant" or forgotten is the  combinatorial rearrangement of a "dictionary" over that of prime module enumeration in Godel's prescriptive dexterity. What is not lost or “spent” is the appropriate gesture that a “hidden” and “irrepressible” lamentation cannot be taught in the structure of the number series reducing lemma, but it has to be learned.The essential idea conjectured in it is that if there is no general solution to Goldbach's conjecture, then there would be a solution to Fermat's Last Theorem, and by  a contractual contradiction since it is known that Fermat's Last Theorem has no solution has through preliminary work by another [ et al.] the Goldbach conjecture must be true in its insidious certainty and  (within a certain understated context) be true here for a proof of existence by the Gödel void. The demonstrative ideal is  that of the geometric quotient, that of a radical  nomenative declaration, that -explains- that a ray is reducible by contractual reduction  from a two-dimensional envelope of  (2)  to a progressively smaller (1) and (0) dimensional free radical exponent through every third (3) two-tilted ray. From this, an algorithm is derived that generates an unbreakable encryption methodology (everything), providing the root clause of data sovereignty and data encryption, Standardization of compact relations of an-infinitive nature and their discrete recombinatorial addressability and assembly.Therefore, compact binary space partitions are  reducible to a maximum of  (5) elements, (to be represented as earth, air, fire, water and wood) with which  the free data right of a flow of / and the level of regulation simply connected / disconnected and (re)established (capable) of analogous regulation of a free radical prime bases  geometrically induced quasilinear 5th order relationships.

Author(s) Details:

Paris Miles Brenden,
Albuquerque, NM, United States of America.

Please see the link here: https://stm.bookpi.org/NTPSR-V8/article/view/7885