Difference between revisions of "2023 AIME I Problems/Problem 9"
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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>? | <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>? | ||
| − | ===Solution=== | + | ===Solution== |
| − | ==Solution 1== | + | ===Solution 1=== |
| − | ==Solution 2== | + | ===Solution 2=== |
Revision as of 13:30, 8 February 2023
Contents
Problem (Unofficial, please update when official one comes out):
is a polynomial with integer coefficients between 
and 
, inclusive. There is exactly one integer 
such that 
. How many possible values are there for the ordered triple 
?
