On the number of solutions to systems of Pell equations |
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| Authors: | Mihai Cipu Maurice Mignotte |
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| Affiliation: | a Institute of Mathematics of the Romanian Academy, PO Box 1-764, RO-014700, Bucharest, Romania
b Université Louis Pasteur, UFR de Mathématiques, 7, rue René Descartes, 67084 Strasbourg Cedex, France |
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| Abstract: | We prove that, for positive integers a, b, c and d with c≠d, a>1, b>1, the number of simultaneous solutions in positive integers to ax2−cz2=1, by2−dz2=1 is at most two. This result is the best possible one. We prove a similar result for the system of equations x2−ay2=1, z2−bx2=1. |
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| Keywords: | Simultaneous Pell equations Linear forms in logarithms |
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