On the Diophantine equation \((x-1)^k+x^k+(x+1)^k=y^n\) (Q2875454)
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scientific article; zbMATH DE number 6330572
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \((x-1)^k+x^k+(x+1)^k=y^n\) |
scientific article; zbMATH DE number 6330572 |
Statements
14 August 2014
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exponential Diophantine equations
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modular forms
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Thue equations
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On the Diophantine equation \((x-1)^k+x^k+(x+1)^k=y^n\) (English)
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In the paper the title equation is solved for the values \(k=2,3,4\). In the proofs, the author uses results on generalized Ramanujan-Nagell equations, and applies the theory of modular forms for certain ternary equations.
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