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manuscripta mathematica

, Volume 65, Issue 4, pp 479–487 | Cite as

The equationxyz=x+y+z=1 in integers of a cubic field

  • Andrew Bremner
Article
  • 22 Downloads

Abstract

We determine all cubic number fields such that the title equation has a solution in the ring of integers of the field.

Keywords

Number Theory Algebraic Geometry Topological Group Number Field Title Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    J. W. S. Cassels, On a diophantine equation,Acta. Arith. 6 (1960), 47–52Google Scholar
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    W. Sierpiński, On some unsolved problems of arithmetic,Scripta Math. 25 (1960), 125–136Google Scholar
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    W. Sierpiński, Remarques sur le travail de M. J. W. S. Cassels “On a diophantine equation”,Acta Arith. 6 (1961), 469–471Google Scholar
  4. 4.
    C. Small, On the equationxyz=x+y+z=1,Amer. Math. Monthly 89 (1982), 736–749Google Scholar
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    R. A. Mollin, C. Small, K. Varadarajan, P. G. Walsh, On unit solutions of the equationxyz=x+y+z in the ring of integers of a quadratic field,Acta. Arith. 48 (1987), 341–345Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Andrew Bremner
    • 1
  1. 1.Department of MathematicsArizona State UniversityTempeUSA

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