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
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.