Difference between revisions of "2023 AIME I Problems/Problem 9"

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==Solution==
 
==Solution==
 
===Solution 1===
 
===Solution 1===
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Pretty sure it's 451
  
 
===Solution 2===
 
===Solution 2===

Revision as of 13:54, 8 February 2023

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

Solution 2