On the Diophantine Equation $D_{1}x^{2}+D_{2}^{m}=4y^{n}$

Maurice Mignotte

Abstract: Consider positive integers $D_{1}$, $D_{2}$ and let $h$ be the class-number of the imaginary quadratic field $Q(\sqrt{-D_{1}\,D_{2}})$. We study the equation $D_{1}x^{2}+D_{2}^{m}=4y^{n}$ when $m$ is an odd integer, $n$ an odd prime number, $\gcd(D_{1}x,D_{2}y)=1$, $n\nomid h$, and also $y>1$.

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