On the Diophantine equation \(cx^2+p^{2m}=4y^n\) (Q2038600)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \(cx^2+p^{2m}=4y^n\) |
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On the Diophantine equation \(cx^2+p^{2m}=4y^n\) (English)
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7 July 2021
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In this paper, the authors study the Diophantine equation \(cx^2 + p^{2m} = 4y^n\) for \(c\) is a square free positive integer and \(p\) is a prime not dividing \(c\) and find all integer solutions. They use the classical result of Bilu, Hanrot and Voutier on primitive divisors in Lehmer sequences [\textit{Yu. Bilu} et al., J. Reine Angew. Math. 539, 75--122 (2001; Zbl 0995.11010)].
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Diophantine equation
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Lehmer number
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primitive divisor
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