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# The Euclidean algorithm for Gaussian integers

@inproceedings{Rolletschek1983TheEA, title={The Euclidean algorithm for Gaussian integers}, author={Heinrich Rolletschek}, booktitle={EUROCAL}, year={1983} }

- Published 1983 in EUROCAL
DOI:10.1007/3-540-12868-9_87

A theorem by Lam$ (1845) answers the following questions: given N, what is the maximum numher of divisions, if the Euclidean algorithm is applied to integers u, v with Neuene0? In this paper we give an analogous result for the Euclidean algorithm applied to Gaussian integers, that is, complex numSers a+bi, where a and b are integers. i. The problem. As is well-known, there exist a number of algebraic extension fields of Q, the field of rational numbers, in which the algebraic integers form a… CONTINUE READING

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