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.
|Number of pages||14|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - Jul 1 2005|
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