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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A finiteness theorem for a class
of exponential congruences


Authors: Marian Vâjâitu and Alexandru Zaharescu
Journal: Proc. Amer. Math. Soc. 127 (1999), 2225-2232
MSC (1991): Primary 11A07
Published electronically: April 9, 1999
MathSciNet review: 1486757
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Abstract | References | Similar Articles | Additional Information

Abstract: For given elements $\alpha _1,\ldots,\alpha _k$ and $\beta$ belonging to the ring of integers $\mathcal{A}$ of a number field we consider the set of all $k-$tuples $(a_1,\ldots,a_k)$ in $\mathbb{N}^k$ for which $\sum _{i=1}^{k}\alpha _i\beta^{a_i}$ divides $\sum _{i=1}^{k}\alpha _i z^{a_i}$ for any $z\in\mathcal{A},$ and prove under some reasonable assumptions that the set of solutions is finite.


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Additional Information

Marian Vâjâitu
Affiliation: Institute of Mathematics of the Romanian Academy, P.O.Box 1-764, 70700 Bucharest, Romania
Email: mvajaitu@stoilow.imar.ro

Alexandru Zaharescu
Affiliation: Massachusetts Institute of Technology, Department of Mathematics, 77 Massachu- setts Avenue, Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Email: azah@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04822-4
PII: S 0002-9939(99)04822-4
Received by editor(s): October 17, 1995
Received by editor(s) in revised form: May 20, 1997, and October 28, 1997
Published electronically: April 9, 1999
Communicated by: William W. Adams
Article copyright: © Copyright 1999 American Mathematical Society