On the equation \(x^ n+(x+a)^ n=y^{2n}+(y+b)^{2n}\)
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.
scientific article; zbMATH DE number 828209