Variants of an Algorithm of J. Stein

Sándor Szabó

In 1961 J. Stein proposed an algorithm to compute the greatest common divisor of two integers. In this paper we point out that similar algorithms exist in the ring of integers of various quadratic number fields and also in the non-commutative ring of the Hurwitz quaternions. The implementations of the algorithms are straightforward. However the procedures vary from case to case.