The Euclidean algorithm for Gaussian integers

  • Heinrich Rolletschek
Algorithms 1 — Miscellaneous
Part of the Lecture Notes in Computer Science book series (LNCS, volume 162)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. F. Caviness, G. E. Collins: Algorithms for Gaussian Integer Arithmetic. In: Proceedings of the 1976 Symposium on Symbolic and Algebraic Computation.Google Scholar
  2. [2]
    H. Hasse: Vorlesunger ueber Zahlentheorie. Springer-Verlag, Berlin. 1964.Google Scholar
  3. [3]
    D. E. Knuth: The Act of Computer Programming. Vol. 2: Seminumerical Algorithms Addison-Wesley, Reading, Massachusetts 1981.Google Scholar
  4. [4]
    H. Rolletschek: The Euclidean Algorithm for Gaussian Integers. Technical report, University of Delaware, to appear.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

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

Personalised recommendations