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Solving Linear Diophantine Equations
2023Linear diophantine equations are at the heart of any unification algorithm for associative and commutative theories. The known algorithms for solving homogeneous linear diophantine equations of Huet and Fortenbacher are presented and their implementation is compared. The algorithms for homogeneous equations are extended to solve inhomogeneous equations,
Guckenbiehl, Thomas, Herold, Alexander
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1988
A linear diophantine equation has the form $$ {a_1}{x_1} + {a_2}{x_2} + ... + {a_n}{x_n} = c $$ where a1, a2,..., an, c are integer constants and x1, x2,..., xn are integer variables. As we saw in Chapter 3, these equations play a very important role in the linear dependence problem.
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A linear diophantine equation has the form $$ {a_1}{x_1} + {a_2}{x_2} + ... + {a_n}{x_n} = c $$ where a1, a2,..., an, c are integer constants and x1, x2,..., xn are integer variables. As we saw in Chapter 3, these equations play a very important role in the linear dependence problem.
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A Diophantine Equation Concerning Linear Recurrences
Periodica Mathematica Hungarica, 1997Let \(G_n ^{(1)}, \ldots, G_n ^{(\nu)}\) and \(H_n^{(1)}, \ldots, H_n ^{(\mu)}\) \((n=0, 1, 2,\ldots)\) be linear recurrence sequences of rational integers with order at least two. For fixed primes \(p_1 , \ldots , p_t \), let \(S\) be the set of integers of the form \(\pm p_1 ^{e_1 } \cdots p_t ^{e_t }\) \((e_i \geq 0)\). The author proves, under some
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On the solutions of the exponential Diophantine equation ax+by= (m2+ 1)z [PDF]
Quaestiones Mathematicae, 2013 Click on the link to view the abstract.Keywords: Exponential Diophantine equation, Terai conjecture, positive integer solution, linear forms in two logarithms, lower bound, primitive divisorQuaestiones Mathematicae 36(2013), 119 ...
, Alain Togbé
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Applications Of Linear Diophantine Equations In Number Theory
Panamerican Mathematical JournalLinear Diophantine equations are one of the most basic types of equation in number theory, which poses the constraint that the solutions must be integers. Any general linear Diophantine equation of the form has integer solutions, and only ones, provided
Dr. Amit Prakash
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The Linear Diophantine Equation in n Variables and Its Application to Generalized Fibonacci Numbers
The Fibonacci quarterly, 1968integers is a problem which may occupy more space in the future development of linear programming,, For n = 2 this is achieved by known methods — either by developing c2 / c j in a continued fraction by Euclid's algorithm or by solving the linear ...
Leon Bernstein
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2015
“I had a very strange dream last night,” Tweedledum said to Tweedledee. “I dreamt that we were not twins but quintuplets.” “What were the names of the others?” asked Tweedledee. “One of them was called Tweedledoo. I don't remember the other two, but they were also Tweedle-something. We had done something that was only possible in a dream. We made the
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“I had a very strange dream last night,” Tweedledum said to Tweedledee. “I dreamt that we were not twins but quintuplets.” “What were the names of the others?” asked Tweedledee. “One of them was called Tweedledoo. I don't remember the other two, but they were also Tweedle-something. We had done something that was only possible in a dream. We made the
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Solution of Systems of Linear Diophantine Equations
2001Two new methods to solve linear systems of Diophantine equations are proposed - modular (CRT) and p-adic (Hensel). Each of them allows to obtain solutions of a system with the size n x m with the complexity O(nsm). For quasi-square systems, the p-adic method allows to obtain solution with the complexity O(n 3), and the modular method with complexity O ...
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On the Exponential Diophantine Equation $F_{n+1}^x - F_{n-1}^x = F_m^y$
Taiwanese Journal of Mathematics, 2022Florian Luca
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