MathDB

35

Part of 1979 IMO Longlists

Problems(1)

Triangle with sides as consecutive terms of a sequence.

Source: ILL 1979-35

6/2/2011
Given a sequence (an)(a_n), with a1=4a_1 = 4 and an+1=an2−2(∀n∈N)a_{n+1} = a_n^2-2 (\forall n \in\mathbb{N}), prove that there is a triangle with side lengths an−1,an,an+1,a_{n-1}, a_n, a_{n+1}, and that its area is equal to an integer.
geometryinductionarea of a triangleHeron's formulainequalities proposedinequalities