Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-01T03:17:34.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear Equations in Integers

Published online by Cambridge University Press:  03 November 2016

Vivian E. Gumbrill  and
Cedric A. B. Smith
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.