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Integer polynomial

Source: All Russian Olympiad 2017,Day2,grade 9,P6

May 3, 2017
quadraticsnumber theoryalgebrapolynomial

Problem Statement

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 ?
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