The Euclidean algorithm for Gaussian integers

  • Heinrich Rolletschek
Algorithms 1 — Miscellaneous

DOI: 10.1007/3-540-12868-9_87

Part of the Lecture Notes in Computer Science book series (LNCS, volume 162)
Cite this paper as:
Rolletschek H. (1983) The Euclidean algorithm for Gaussian integers. In: van Hulzen J.A. (eds) Computer Algebra. EUROCAL 1983. Lecture Notes in Computer Science, vol 162. Springer, Berlin, Heidelberg

Abstract

A theorem by Lamé (1845) answers the following questions: given N, what is the maximum number of divisions, if the Euclidean algorithm is applied to integers u, v with N≥u≥n≥0? In this paper we give an analogous result for the Euclidean algorithm applied to Gaussian integers, that is, complex numbers a+bi, where a and b are integers.

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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Heinrich Rolletschek
    • 1
  1. 1.Department of Computer and Information SciencesUniversity of DelawareNewarkUSA

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