2023 AIME I Problems/Problem 9

Problem (Unofficial, please update when official one comes out):

$P(x) = x^3 + ax^2 + bx + c$ is a polynomial with integer coefficients in the range $[-20, -19, -18\cdots 18, 19, 20]$ , inclusive. There is exactly one integer $m \neq 2$ such that $P(m) = P(2)$ . How many possible values are there for the ordered triple $(a, b, c)$ ?

Solution

Solution 1

Pretty sure it's 451

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2023 AIME I Problems/Problem 9

Contents

Problem (Unofficial, please update when official one comes out):

Solution

Solution 1

Solution 2