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MathNet 1990 — Part 01 Question 12

Math Olympiad Vault · MathNet 1990 — Part 01

Question 12

Let $*$ denote an operation, assigning a real number $a * b$ to each pair of real numbers $(a, b)$ (e.g., $a * b = a + b^{2} - 17$). Devise an equation which is true (for all possible values of variables) provided the operation $*$ is commutative or associative and which can be false otherwise.