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ON SOME ARITHMETICAL PROPERTIES OF SOLUTIONS OF DECOMPOSABLE FORM EQUATIONS

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Abstract

Abstract. We study some fine arithmetic properties of the components of solutions of a decomposable form equation. Lower growth rates for the greatest prime factor of a component are obtained for density 1 of the solutions. Also, high pure powers are shown to occur rarely. Computations illustrate the applicability of our results; for example, to the study of units in abelian group rings. 1

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.160.5343
Provided by: CiteSeerX
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