On the Diophantine equation \((x^ k-1)(y^ k-1)=(z^ k-1)\). (Q1890409)
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scientific article; zbMATH DE number 2124626
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \((x^ k-1)(y^ k-1)=(z^ k-1)\). |
scientific article; zbMATH DE number 2124626 |
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On the Diophantine equation \((x^ k-1)(y^ k-1)=(z^ k-1)\). (English)
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3 January 2005
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The author investigates 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, where \(k\geq 3\). Moreover he proves results related to variants of the problem of Diophantus.
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linear forms in two logarithms
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exponential Diophantine equation
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