2

Part of 1908 Eotvos Mathematical Competition

Problems(1)

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

Source: Eotvos 1908 p2

n

be an integer greater than

2

. Prove that the

n

th power of the length of the hypotenuse of a right triangle is greater than the sum of the

n

th powers of the lengths of the legs.

geometryinequalitiesgeometric inequalitynumber theory