SEEMOUS 2013 Problem 1

Find all continuous functions $f:[1,8]\to\mathbb R$ , such that $\int^2_1f(t^3)^2dt+2\int^2_1f(t^3)dt=\frac23\int^8_1f(t)dt-\int^2_1(t^2-1)^2dt.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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