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

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==Problem (Unofficial, please update when official one comes out):==
 
==Problem (Unofficial, please update when official one comes out):==
  
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<math>P(x) = x^3 + ax^2 + bx + c</math> is a polynomial with integer coefficients between <math>-20</math> and <math>20</math>, inclusive. There is exactly one integer <math>m</math> such that <math>P(m) = P(2)</math>. How many possible values are there for the ordered triple <math>(a, b, c)</math>?
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<math>P(x) = x^3 + ax^2 + bx + c</math> is a polynomial with integer coefficients in the range<math>[-20, -19, -18\cdots 18, 19, 20]</math>, inclusive. There is exactly one integer <math>m \neq 2</math> such that <math>P(m) = P(2)</math>. How many possible values are there for the ordered triple <math>(a, b, c)</math>?
  
 
==Solution==
 
==Solution==

Revision as of 14:38, 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

Solution 2

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