On Fermat's Last Theorem (Q5899824)

The following result is proved by elementary means: Let \(x^ n+y^ n=z^ n\) where x, y, z and \(n\geq 2\) are positive integers such that \(x<y<z\); then \(z<x^{1+1/(n-1)}.\) This inequality is stronger than that proved by \textit{K. Bialek} [Elem. Math. 43, No.3, 78-83 (1988; see the preceding review)]; namely, \(x^ 2>2z+1\) for \(n\geq 3\).