A note on the diophantine equation \((a^n-1)(b^n-1)= x^2\) (Q377815)
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scientific article; zbMATH DE number 6223888
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the diophantine equation \((a^n-1)(b^n-1)= x^2\) |
scientific article; zbMATH DE number 6223888 |
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A note on the diophantine equation \((a^n-1)(b^n-1)= x^2\) (English)
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7 November 2013
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Under the assumption that \(a,b\) are positive integers greater than one such that the exponent of \(2\) in the prime factorization of \((a-1)(b-1)\) is odd, all positive integer solutions \((x,n)\) to the equation in the title are determined. The main tool in the proof is the theory of Pellian equations. Beside this, the author uses some results concerning certain concrete elliptic and hyperelliptic diophantine equations, as well.
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exponential diophantine equation
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square classes of sequence
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