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61.6 Solving linear diophantine equations using matrices

Published online by Cambridge University Press:  22 September 2016

Malcolm Macnicol
Malcolm Macnicol*
Affiliation:
56 Nethercliffe Avenue, Netherlee, Glasgow G44 3UL
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Extract

The method described in this note is, like other standard approaches, based on the “Euclidean algorithm”, but a matrix format is used (assuming the coefficients have no common factor) to reduce the equation ax + by = c to a form such as

or a similar equation with matrix (k l),(k −l) or (−1 k). The following lemma is easily verified.

Type
Notes
Information
The Mathematical Gazette , Volume 61 , Issue 416 , June 1977 , pp. 130 - 132
Copyright
Copyright © Mathematical Association 1977

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