Abstract
LetD be a positive square free integer, and leth(−D) denote the class number of\(\mathbb{Q}(\sqrt {--D} )\). Furthermore letp be an odd prime with\(p\not |h(--D)\). In this note we prove that ifp∈ {5, 7} orp>3·106, then the equation\(x^2 + 4D = y^p ,{\text{ }}2\not |xy\), has no positive integer solution (x, y).
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References
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