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On the Diophantine equation \(x^2+3^a41^b=y^n\) - MaRDI portal

On the Diophantine equation \(x^2+3^a41^b=y^n\) (Q2221026)

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On the Diophantine equation \(x^2+3^a41^b=y^n\)
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    On the Diophantine equation \(x^2+3^a41^b=y^n\) (English)
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    25 January 2021
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    There is an extensive literatue of the Ramanujan-Nagell equation \[x^2+C=y^n\] with \(n\geq 3\). Several authors solved this equation for special values of \(C\). In a recent paper \textit{H. Zhu} et al. [Period. Math. Hung. 70, No. 2, 233--247 (2015; Zbl 1349.11078)] the authors investigated positive integer solutions for \(C=2^ap^b\) with any odd prime \(p\).\par In the present paper the authors describe the positive integer solutions of \[x^2+3^a41^b=y^n\] with \(n\ge 3\), \(\gcd (x,y)=1\).
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    Diophantine equations
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    Ramanujan-Nagell equations
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    primitive divisor theorem
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