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Linear Equations in Integers

Published online by Cambridge University Press:  03 November 2016

Vivian E. Gumbrill  and
Cedric A. B. Smith
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Extract

The process normally given in books for the solution of linear equation in integer unknowns is dependent on the theory of continued fraction. There is however no need for any such special theory, and the continue fraction process is not the quickest possible.

But a knowledge of a simpler process seems to be far from general, and it would seem to be of value to give an account of one such process here, and to see how it may be given a simple arrangement. In addition, as we will see this process has the good point that it may be used without difficulty to give the general solution of equations with more than two unknowns, and systems of such equations.

Type
Research Article
Information
The Mathematical Gazette , Volume 28 , Issue 278 , February 1944 , pp. 22 - 26
Copyright
Copyright © Mathematical Association 1944

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References

page no 22 note * Lehmer, D. H. gives a process very like ours, but using determinants. See “note on the linear Diophantine equation”, Amer. Math. Mon., vol. 48 (1941 pp. 240–246 CrossRefGoogle Scholar.

page no 23 note * The arrangement (though not the explanation) is in effect that of Aitken, A. C., “Expansion of a certain triple product matrix”, Proc. Roy. Soc. Ed., lvii, (1937), p. 172 Google Scholar.