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On the Diophantine equation $$x^2+q^{2k+1}=y^n$$. (English) Zbl 1037.11021
It is proved that if $$q$$ is an odd prime, $$q \not \equiv 7 \pmod 8$$, $$n$$ is an odd integer $$> 5$$, $$n$$ is not a multiple of 3 and $$(h,n) = 1$$, where $$h$$ is the class number of the field $$\mathbb{Q}(\sqrt{-q})$$, then the Diophantine equation $$x^2 + q^{2k+1} = y^n$$ has exactly two families of solutions $$(q,n,k,x,y)$$.

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