MathDB
a^n > b^n + c^n if a^2=b^2+c^2

Source: Eotvos 1908 p2

September 8, 2024
geometryinequalitiesgeometric inequalitynumber theory

Problem Statement

Let nn be an integer greater than 22. Prove that the nnth power of the length of the hypotenuse of a right triangle is greater than the sum of the nnth powers of the lengths of the legs.