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2023 AIME I Problems/Problem 9

Revision as of 14:30, 8 February 2023 by Chem1kall (talk | contribs) (→‎Solution 1)

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

$P(x) = x^3 + ax^2 + bx + c$ is a polynomial with integer coefficients between $-20$ and $20$, inclusive. There is exactly one integer $m$ such that $P(m) = P(2)$. How many possible values are there for the ordered triple $(a, b, c)$?

Solution

Solution 1

Solution 2

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