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f(x) = x^3 +px^2 +qx+r , f(\sqrt3) = 0, f(s) = 506

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2022 p2

March 26, 2024
algebrapolynomial

Problem Statement

Find all functions ff, of the form f(x)=x3+px2+qx+rf(x) = x^3 +px^2 +qx+r with pp, qq and rr integers, such that f(s)=506f(s) = 506 for some integer ss and f(3)=0f(\sqrt3) = 0.
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