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On some arithmetical properties of solutions of decomposable form equations

Published online by Cambridge University Press:  22 June 2005

GRAHAM EVEREST  and
KALMAN GYÖRY
GRAHAM EVEREST
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ. e-mail: [email protected]
KALMAN GYÖRY
Affiliation:
Institute of Mathematics, University of Debrecen, Number Theory Research Group of the HAS, H-4010 Debrecen, Pf.12. Hungary. e-mail: [email protected]
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 1 , July 2005 , pp. 27 - 40
Copyright
2005 Cambridge Philosophical Society

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