On the Diophantine equation \(x^ 2+a^ 2=2y^ p\).
The author combines lower bounds for two logarithms (in the complex case) with elementary arguments to provide an effective method to solve completely instances of the exponential Diophantine equations \(x^2+a^2=2y^p\) and \(x^2+a^2=y^p\). As examples, he solves completely the first equation for \(a\) odd, \(3\leq a \leq 305\), and the second one for \(a\) odd, \(3\leq a \leq 501\).
scientific article; zbMATH DE number 2124645
scientific article