ABSTRACT. A complete (intrinsic) solution to the Rivlin problem is given in the space C_{2}[a, b] of continuous functions on [a, b] with the L_{2}-norm. A brief survey is also given of what is known in the spaces C_{p}[a, b], 1 ≤ p ≤ ∞, p ≠ 2. In each of these spaces only partial results are known.