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