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RU-ALLRUSSIAN 2017 Problem 96

    a,b,ca,b,c - different natural numbers. Can we build quadratic polynomial P(x)=kx2+lx+mP(x)=kx^2+lx+m , with k,l,mk,l,m are integer, k>0k>0 that for some integer points it get values a3,b3,c3a^3,b^3,c^3 ?

    Dataset text AI-MO AoPS. Quoted with source.

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