On a kind of superelliptic Diophantine equations (Q2759819)

Let \(a\), \(d\), \(k\) be positive integers with \(d\) square free. Let \(f(x)= da^2 x^{2k}+ a_{2k-1}x^{2k-1}+\cdots+ a_0\in \mathbb{Z}[x]\). In this paper the author gives an algorithm for finding the integer solutions \((x,y)\) of the equation \(f(x)= dy^2\). A similar algorithm has been given by \textit{L. Szalay} [Acta Acad. Paedagog. Agriensis, Sec. Math. (N.S.) 27, 19-24 (2000; Zbl 0973.11039)].