olymmath

VMO 2006 Problem 5

    Find all polynomyals P(x)P(x) with real coefficients which satisfy the following equality for all real numbers xx : P(x2)+x(3P(x)+P(−x))=(P(x))2+2x2.P(x^2)+x(3P(x)+P(-x))=(P(x))^2+2x^2 .

    Dataset text AI-MO AoPS. Quoted with source.

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