On the Diophantine equation \(y^n=f(x)^n+g(x)\) (Q2910306)

In 2002, \textit{L. Szalay} gave an algorithm for the computation of integer solutions of the Diophantine equation \(y^p = x^{kp}+a_{kp-1} x^{kp-1}+\cdots + a_0\) [Bull. Greek Math. Soc. 46, 23--33 (2002; Zbl 1014.11020)]. In the paper under review, the authors deal with the more general Diophantine equation \(y^n = f(x)^n+g(x)\), where \(n\) is a positive integer, \(f(x)\) and \(g(x)\) are non-zero rational polynomials, \(f(x)\) has a positive leading coefficient and \(\deg g(x) \leq (n-1)+\deg f(x)\). They present an algorithm for the computation of the integer solutions of this equation which is simpler than that of Szalay.