Viewing a response to: @xeliram/ecuaciones-diofanticas-lineal. spanish · @ · 58 days ago. @xeliram, go and place your daily vote for Steem on . Optimización por Enjambre de Partículas Discreto en la Solución Numérica de un Sistema de Ecuaciones Diofánticas Lineales. Iván Amaya a, Luis Gómez b. Ecuaciones diofánticas lineales, soluciones cor- tas, algoritmo de reducción de la base. 1. Introduction. One can solve the linear Diophantine equation. aT x = b.

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Ecuaciones diofánticas lineales. Tabla con algoritmo de Euclides.

This system is equivalent, by Gaussian reduction, to the Its general solution is given by: Areas such rcuaciones cryptography, integer factorization, number theory, algebraic geometry, control theory, data dependence on supercomputers, communications, and so on, are some examples [1].

The second one can also be a random vector, but it can be assumed as zero for the first iteration, in order to keep it simple. Linear Diophantine equations; objective function; optimization; particle swarm.

It contains all integral numbers from negative infinity to positive infinity. Chapter 3 Continuity In diofantticas chapter we begin by defining the fundamental notion of continuity for real valued functions of a single diiofanticas variable. In order to solve this problem with the discrete PSO algorithm, the following objective function is created: Moreover, it was found that the convergence time and the number of iterations are random variables that mainly depend on factors such as the algorithm parameters, the initial swarm and the size of the system.


Moreover, an initial speed of zero can be defined for the particles.

Animal Biodiversity and Conservation, A first stage is given by the random assignation of a swarm of user defined integers. Moreover, all global minimizers of g are solutions of eq. Also, it was observed diofanitcas it is possible to solve this optimization problem without using conventional approaches.

Therefore, if a linear Diophantine diofanticxs with two unknowns has a solution in the integers, then it has infinite solutions of this kind. The following result is achieved: Two factorizations of an element of B are regarded as essentially the same if More information. Their duration, however, varied from s, with iterations, and up to s, with iterations.


A linear Diophantine equation, with unknowns, is defined by eq. This procedure is iterative and is repeated until the convergence criteria are met, or until all solutions in the search domain are found.

If the function g defined in 5 has a global minimum in X and this value is zero, then eq.

A first stage is given by the random assignation of a swarm of user defined integers. Our first test checks.

Ecuaciones diofánticas lineales. Tabla con algoritmo de Euclides.

A basic result of the mathematical analysis of the algorithm establishes that if is a compact set i. Likewise, the definition of these values is subject to previous knowledge of the diofatnicas function fitnessas well as to the presence of restrictions.

It has been conjectured that there are infinitely many primes of the form n. Also, it was observed that it is possible to solve this optimization problem without using conventional approaches.


The discrete PSO algorithm reports that after 20 or more runs, for different ecuacoines sizes and parameters, it was not possible to find an answer. This also applies for linear systems with this kind of equations i. This section shows the results achieved after solving some systems of linear Diophantine equations, as an example of the method.

Our first test checks More information. Identify and More information. Ecuaaciones immediate consequence of theorem 4 is that if the system 8 has a solution inthen the global minimum of defined in 9 exists and it is zero; moreover, the following result exists: Moreover, all global minimizers of are solutions of eq.

Initially, some basic and necessary related concepts are laid out, and then the viability of using diofwnticas numeric strategy is shown through some examples.

Algebra I Part IV: For the case of systems of Diophantine equations, unlike the particular case of an equation with two unknowns, the fact that a solution exists does not imply that others do, and even less that an infinite number exists.

His research interests include microwave heating, global optimisation, heat transfer linealds polymers.