Calculating the General Solution of a Linear Diophantine Equation

1967 ◽  
Vol 74 (8) ◽  
pp. 955 ◽  
Author(s):  
James Bond
Keyword(s):  
General Solution ◽  
Diophantine Equation ◽  
Linear Diophantine Equation

A Simple Algorithm for Solving the n-Dimensional linear Diophantine Equation

1975 ◽  
Vol 68 (1) ◽  
pp. 56-57
Author(s):  
Aziz Ibrahim ◽  
Edward J. Gucker
Keyword(s):  
General Solution ◽  
Diophantine Equation ◽  
Simple Algorithm ◽  
Euclidean Algorithm ◽  
Transformation Matrix ◽  
Matrix Transformation ◽  
Two Dimensional ◽  
Linear Diophantine Equation ◽  
The Given

In an earlier paper, we showed that the Euclidean algorithm could be written as a matrix transformation to obtain the solution of a two-dimensional Diophantine equation (Ibrahim and Gucker, 1972). In the present paper, we generalize this approach to n-dimensional and also simplify the algorithm that produces the transformation matrix. We also show that the final matrix contains the most general solution of the given Diophantine equation.

Inside factorial monoids and the Cale monoid of a linear Diophantine equation

2019 ◽  
Vol 531 ◽  
pp. 125-140
Author(s):  
Pedro A. García-Sánchez ◽  
Ulrich Krause ◽  
David Llena
Keyword(s):  
Diophantine Equation ◽  
Linear Diophantine Equation

The Linear Diophantine Equation

1981 ◽  
Vol 88 (3) ◽  
pp. 200 ◽  
Author(s):  
Stanley Kertzner
Keyword(s):  
Diophantine Equation ◽  
Linear Diophantine Equation
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