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MathNet 2020 — Math Olympiad Vault — Part 01 Question 85

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 01

Question 85

Find all polynomial functions $P(x, y)$ with real coefficients which for all real numbers $x$ and $y$ satisfy
$$
P(x + y, x - y) = 2P(x, y).
$$