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Find all count. functions (Titu Andreescu)

Source: RomNO 2003, grade xii, p.2

August 27, 2019
functionreal analysisintegrationDefinite integralTitu Andreescu

Problem Statement

Let be an odd natural number n≥3. n\ge 3. Find all continuous functions f:[0,1]⟶R f:[0,1]\longrightarrow\mathbb{R} that satisfy the following equalities. \int_0^1 \left( f\left(\sqrt[k]{x}\right) \right)^{n-k} dx=k/n, \forall k\in\{ 1,2,\ldots ,n-1\}
Titu Andreescu
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