Abstract
In two papers I have proved that there are only a finite number of quadratic fields [6] and of cyclic cubic fields [7] in which Euclid's algorithm (E.A.) holds. Davenport has shown by a different method that there are only a finite number of quadratic fields [1, 2], of non-totally real cubic fields [3, 4] and of totally complex quartic fields in which E.A. holds.
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