Mazur, Marcin; Smoktunowicz, Agata On the equation \(x^ n+(x+a)^ n=y^{2n}+(y+b)^{2n}\). (English) Zbl 0839.11015 Indag. Math., New Ser. 6, No. 3, 309-314 (1995). Let \(n \geq 2\). It is proved that the equation in the title with \(a,b\) odd has only finitely many nontrivial solutions in integers \(x,y\). When \(a = b = 1\), the equation admits only the trivial solutions \(x = 0\), \(y \in \{0, -1\}\) or \(x = - 1\), \(y \in \{0, -1\}\) with \(n\) even. Reviewer: E.L.Cohen (Ottawa) MSC: 11D61 Exponential Diophantine equations 11D41 Higher degree equations; Fermat’s equation Keywords:higher degree diophantine equations PDFBibTeX XMLCite \textit{M. Mazur} and \textit{A. Smoktunowicz}, Indag. Math., New Ser. 6, No. 3, 309--314 (1995; Zbl 0839.11015) Full Text: DOI