On the length of arithmetic progressions in linear combinations of S-units |
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| Authors: | Lajos Hajdu Florian Luca |
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| Institution: | 1. Number Theory Research Group of the Hungarian Academy of Sciences, Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary
2. Mathematical Institute, UNAM, Ap. Postal 61-3 (Xangari), CP 58 089, Morelia, Michoacán, Mexico
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| Abstract: | Recent finiteness results concerning the lengths of arithmetic progressions in linear combinations of elements from finitely
generated multiplicative groups have found applications to a variety of problems in number theory. In the present paper, we
significantly refine the existing arguments and give an explicit upper bound on the length of such progressions. |
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