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find polynomials

Source: Mathematics Regional Olympiad of Mexico Southeast 2018 P6

October 24, 2021
algebrapolynomial

Problem Statement

Find all polynomials p(x)p(x) such that for all reals a,ba, b and cc, with a+b+c=0a+b+c=0, satisfies
p(a3)+p(b3)+p(c3)=3p(abc)p(a^3)+p(b^3)+p(c^3)=3p(abc)
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