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On Unit Solutions of the Equation xyz = x + y + z in Not Totally Real Cubic Fields

Published online by Cambridge University Press:  20 November 2018

Liang-Cheng Zhang  and
Jonathan Gordon
Liang-Cheng Zhang
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, USA
Jonathan Gordon
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, USA
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Abstract

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It is shown that the equation xyz = x+y+z has unit solutions in only four not totally real cubic fields: two fields which are real and two fields which are imaginary. These fields are then listed.

Keywords

11D2511R2711R16.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 141 - 144
Copyright
Copyright © Canadian Mathematical Society 1991

References

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