MathDB
Natural functions

Source: RMO 2003, District Round

May 29, 2006
functiongeometry3D geometryalgebra proposedalgebra

Problem Statement

Find all functions f:N∗→N∗\displaystyle f : \mathbb N^\ast \to \mathbb N^\ast (N∗={1,2,3,…}\displaystyle N^\ast = \{ 1,2,3,\ldots \}) with the property that, for all n≥1\displaystyle n \geq 1, f(1)+f(2)+…+f(n) f(1) + f(2) + \ldots + f(n) is a perfect cube ≤n3\leq n^3. Dinu Teodorescu
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