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Solving Thue equations without the full unit group

Guillaume Hanrot 1
1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The main problem when solving a Thue equation is the computation of the unit group of a certain number field. It is shown that the knowledge of a subgroup of finite index is in fact sufficient. Two examples linked with the primitive divisor problem for Lucas and Lehmer sequences are given. || La principale difficulté lors de la résolution d'une équation de Thue réside dans le calcul du groupe des unités du corps de nombres associé. On montre qu'il suffit en fait de connaître un sous-groupe d'indice fini de ce groupe. On donne deux exemples li
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Submitted on : Tuesday, September 26, 2006 - 8:51:07 AM
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  • HAL Id : inria-00099118, version 1



Guillaume Hanrot. Solving Thue equations without the full unit group. Mathematics of Computation, American Mathematical Society, 2000, 69 (229), pp.395-405. ⟨inria-00099118⟩



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