Diophantine equations with Euler polynomials (Q2868211)

In the main result (Theorem 1.1) of the paper under review, the authors describe the decomposition properties of the Euler polynomials. As an application, using among other things the ineffective finiteness criterion of \textit{Y. F. Bilu} and \textit{R. F. Tichy} [Acta Arith. 95, No. 3, 261--288 (2000; Zbl 0958.11049)] for separable diophantine equations, the authors prove a finiteness result on the equation NEWLINE\[NEWLINE -1^k + 2^k - \ldots + (-1)^x x^k = g(y),NEWLINE\]NEWLINE where \(k\geq 7\) and \(g(x)\) is a polynomial with rational coefficients.