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On numbers which are differences of two conjugates of an algebraic integer

Published online by Cambridge University Press:  17 April 2009

Artūras Dubickas
Artūras Dubickas
Affiliation:
Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius 2600, Lithuania, e-mail: arturas.dubickas@maf.vu.lt
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Abstract

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We investigate which numbers are expressible as differences of two conjugate algebraic integers. Our first main result shows that a cubic, whose minimal polynomial over the field of rational numbers has the form x3 + px + q, can be written in such a way if p is divisible by 9. We also prove that every root of an integer is a difference of two conjugate algebraic integers, and, more generally, so is every algebraic integer whose minimal polynomial is of the form f (xe) with an integer e ≥ 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 439 - 447
Copyright
Copyright © Australian Mathematical Society 2002

References

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