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The Linear Diophantine Equation
The American Mathematical Monthly, 1981(1981). The Linear Diophantine Equation. The American Mathematical Monthly: Vol. 88, No. 3, pp. 200-203.
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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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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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A Note on the Linear Diophantine Equation
The American Mathematical Monthly, 1941(1941). A Note on the Linear Diophantine Equation. The American Mathematical Monthly: Vol. 48, No. 10, pp. 662-666.
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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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A Forward Approach for Solving Linear Diophantine Equation
International Journal of Mathematical Education in Science and Technology, 2020Yiu Kwong MAN
exaly
Solving a System of Linear Diophantine Equations With Lower and Upper Bounds on the Variables
Mathematics of Operations Research, 2000Karen Aardal, Arjen K. Lenstra
exaly