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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)

##### MSC:
 11D41 Higher degree equations; Fermat’s equation 11D61 Exponential Diophantine equations
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##### References:
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