Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
Let \(D\) be a non-square integer, and let \(D_1\), \(D_2\) be integers satisfying \(D_1 D_2= D\) with \(D_1>0\) and \(\gcd(D_1, D_2) =1\). Let \(k\) be an integer with \(|k|> 1\) and \(\gcd(D, k)=1\). The author gives some explicit formulas for all integer solutions \((x, y, z)\) of the equation in the title when \(\gcd(x, y) =1\), \(z>0\) and \(\lambda=1\text{ or }4\).
scientific article; zbMATH DE number 844632