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On the diophantine equation (x − 1)(y − 1) = (z − 1) |
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| Authors: | Yann Bugeaud |
| Institution: | Université Louis Pasteur, UFR de Mathématiques, 7, rue René Descartes, 67084 Strasbourg, France |
| Abstract: | Let k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integers (a, b) such that any of the three numbers a + 1, b + 1, and ab + 1 is a k-th power. We further investigate several related questions. |
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