On the Diophantine equation \((a^n - 1)(b^n -1) = x^2\) (Q2915401)
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scientific article; zbMATH DE number 6083234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \((a^n - 1)(b^n -1) = x^2\) |
scientific article; zbMATH DE number 6083234 |
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17 September 2012
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exponential diophantine equations
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Pell equations
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On the Diophantine equation \((a^n - 1)(b^n -1) = x^2\) (English)
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Generalizing earlier results from the literature, the authors show that for positive integers \(a\) and \(b\) satisfying certain congruence conditions modulo 2, 4, or 5, the title equation has no solutions in positive integers \(n>2\) and \(x\). In the proof beside tools from the theory of Pellian equations, results concerning ternary equations of signature \((n,n,2)\) are also used.
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