Developments on Beal Conjecture from Pythagoras´ and Fermat´s Equations
Leandro Torres Di Gregorio
Issue:
Volume 2, Issue 5, October 2013
Pages:
149-155
Received:
20 August 2013
Published:
20 September 2013
Abstract: The Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the number theory´s field. It states that, for X, Y, Z, n1, n2 and n3 positive integers with n1, n2, n3 > 2, if Xn1 +Yn2=Zn3 then X, Y, Z must have a common prime factor. This article aims to present developments on Beal Conjecture, obtained from the correspondences between the real solutions of the equations in the forms A2 + B2 = C2 (here simply refereed as Pythagoras´ equation), δn + γn=αn (here simply refereed as Fermat´s equation) and Xn1 +Yn2=Zn3 (here simply referred as Beal´s equation). Starting from a bibliographical research on the Beal Conjecture, prime numbers and Fermat's Last Theorem, these equations were freely explored, searching for different aspects of their meanings. The developments on Beal Conjecture are divided into four parts: geometric illustrations; correspondence between the real solutions of Pythagoras´ equation and Fermat's equation; deduction of the transforms between the real solutions of Fermat's equation and the Beal´s equation; and analysis and discussion about the topic, including some examples. From the correspondent Pythagoras´ equation, if one of the terms A, B or C is taken as an integer reference basis, demonstrations enabled to show that the Beal Conjecture is correct if the remaining terms, when squared, are integers.
Abstract: The Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the number theory´s field. It states that, for X, Y, Z, n1, n2 and n3 positive integers with n1, n2, n3 > 2, if Xn1 +Yn2=Zn3 then X, Y, Z must have a common prime factor. This article aims to present developments on Beal Conjecture, obtaine...
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On Some Properties of Hollow and Hollow Dimension Modules
Majid Mohammed,
Abd Ghafur Bin Ahmad
Issue:
Volume 2, Issue 5, October 2013
Pages:
156-161
Received:
18 August 2013
Published:
30 September 2013
Abstract: No doubt, a notion of the hollow dimension modules can constitute a very important situation in the module theory. Therefore, our work presents a key role mainly in some properties and characterizations of hollow and hollow dimension module. We prove that if R be a V-ring and M is semisimple with indecomposable property, then M is hollow module. Also we study characterization the relation between lifting property and hollow-lifting module. We prove that if M is a nonzero indecomposable and lifting module over a commutative noetherian ring R then M is hollow module. Let M be an R-module and N be a submodule of M if hdim(M) = hdim(M/N) + hdim(N), then M is supplemented module.
Abstract: No doubt, a notion of the hollow dimension modules can constitute a very important situation in the module theory. Therefore, our work presents a key role mainly in some properties and characterizations of hollow and hollow dimension module. We prove that if R be a V-ring and M is semisimple with indecomposable property, then M is hollow module. Al...
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A Decomposable Computer Oriented Method for Solving Interval LP Problems
Sharmin Afroz,
M. Babul Hasan
Issue:
Volume 2, Issue 5, October 2013
Pages:
162-168
Received:
26 September 2013
Published:
30 October 2013
Abstract: The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.
Abstract: The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solvi...
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The Case against Educated Mathematical Dogma (Precise Mathematical Pi Value by Finite Equation =3.14159292035) 3+(1/(7+1/16)) Precise Finite Value
Issue:
Volume 2, Issue 5, October 2013
Pages:
169-173
Received:
30 September 2013
Published:
10 November 2013
Abstract: The relevance of this paper to current approximate mathematics and the sciences is a massive change, because this mathematics binds numbers in the rationality of a finite space of the primordial constriction from 4 to 3 coordinates, which leads to a specific calculable mathematical π, correct trigonometry, and the divergence of 1:3, and the placement of all prime numbers. We have also separately produced the continuous Prime number sieve at 1/3, 2/3, 5/ 6 and 1/6 (den- otter continuous sieve of Prime numbers). The method of the sieve is impossible for current mathematics to understand as the discoverer is uneducated and hard to comprehend except by chalk board. It is a continuous sieve accurate till billions. There has never been in the history of mathematics the mathematical derivation of the π value by precise mathematics of space constriction of value 4 to value 3. Current acceptable π value is by dogma and tradition and is not correct except by dogma, and does not have a pure mathematical derivation. Words like transcendental, are a dogma, and approximate mathematics.
Abstract: The relevance of this paper to current approximate mathematics and the sciences is a massive change, because this mathematics binds numbers in the rationality of a finite space of the primordial constriction from 4 to 3 coordinates, which leads to a specific calculable mathematical π, correct trigonometry, and the divergence of 1:3, and the placeme...
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