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Polynomial with integer roots

Source: St Petersburg Olympiad 2018, , Grade 10, P4

June 21, 2018
algebrapolynomialabstract algebra

Problem Statement

f(x)f(x) is polynomial with integer coefficients, with module not exceeded 5āˆ—1065*10^6. f(x)=nxf(x)=nx has integer root for n=1,2,...,20n=1,2,...,20. Prove that f(0)=0f(0)=0
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