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f(x)f(x + 3) = f(x^2 + x + 3)

Source: Polish MO Recond Round 1986 p5

September 9, 2024
algebrapolynomial

Problem Statement

Prove that if the polynomial f f which is not identical to zero satisfies for every real x x the equality f(x)f(x+3)=f(x2+x+3), f(x)f(x + 3) = f(x^2 + x + 3), then it has no real roots .
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