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TH-TMO 2020 Problem 7

    Determine all functions f:R→Zf:\mathbb{R}\to\mathbb{Z} satisfying the inequality (f(x))2+(f(y))2≤2f(xy)(f(x))^2+(f(y))^2 \leq 2f(xy) for all reals x,yx,y .

    Dataset text AI-MO AoPS. Quoted with source.

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