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[3] viXra:2304.0231 [pdf] submitted on 2023-04-30 13:55:48
Authors: Seung-pyo Hong
Comments: 26 Pages.
The method of factoring large numbers is not known; however, using the method included in this document, it is possible to make a small number of judgments in a short time. The programming language is composed of Java.
Category: Algebra
[2] viXra:2304.0228 [pdf] submitted on 2023-04-29 06:19:55
Authors: Michael Reed
Comments: 28 Pages.
Tools built on these foundations enable computations based on multi-linear algebra and spin groups using the geometric algebra known as Grassmann algebra or Clifford algebra. This foundation is built on a direct-sum parametric type system for tangent bundles, vector spaces, and also projective and differential geometry. Geometric algebra is a mathematical foundation for differential geometry, which can be used to simplify the Maxwell equations to a single wave equation due to the geometric product. Introduction of geometric algebra to engineering science disciplines will be easier with programmable foundations.In order to devise an expressive and performance oriented language for efficient discrete differential geometric algebra with the Grassmann elements, an efficient computer algebra representation was programmed. With this unifying mathematical foundation, it is possible to improve efficiency of multi-disciplinary research using geometric tensor calculus by relying on universal mathematical principles. Tools built on universal differential geometric algebra provide a natural geometric language for the Helmholtz decomposition and Hodge-DeRahm co/homology.
Category: Algebra
[1] viXra:2304.0019 [pdf] replaced on 2026-04-06 01:35:28
Authors: Kurmet Sultan
Comments: 15 Pages.
A simple proof of Fermat’s Last Theorem (FLT) for the cube is obtained using the binomial expansion formula. The difference of twonatural numbers having equal natural powers necessarily has a representation according to the formula of an incomplete binomial. It isproved that the cube of a natural number cannot be represented as an incomplete binomial, which means a simple proof of FLT for n = 3 is obtained.
Category: Algebra
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