On a diophantine equation. (English) Zbl 0905.11018

The equation \(x^2+ 3^{2k} =y^n\) where \(n\geq 3\) is studied. For \(n=3\), it is proved that it has a solution only if \(k\equiv 2\pmod 3\) and then it is unique. If this equation has a solution for \(n>3\), then \(n\) is odd and \(k=2^\delta \kappa\), where \(\delta\geq 1\), \((2,\delta) =1\), \(\kappa\equiv 15\pmod{20}\) and all the prime divisors \(p\) of \(n\) are congruent to \(11 \pmod {12}\).
Reviewer: E.L.Cohen (Ottawa)


11D41 Higher degree equations; Fermat’s equation
11D61 Exponential Diophantine equations


Zbl 0905.11017
Full Text: DOI


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