olymmath

UZ-MO 2013 Problem 3

    Find all functions f:Q→Qf:Q\rightarrow Q such that f(x+y)+f(y+z)+f(z+t)+f(t+x)+f(x+z)+f(y+t)≥6f(x−3y+5z+7t)f(x+y)+f(y+z)+f(z+t)+f(t+x)+f(x+z)+f(y+t)\ge 6f(x-3y+5z+7t) for all x,y,z,t∈Q.x,y,z,t\in Q.

    Dataset text AI-MO AoPS. Quoted with source.

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