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):== | ||
− | <math>P(x) = x^3 + ax^2 + bx + c</math> is a polynomial with integer coefficients | + | <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 13:38, 8 February 2023
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[hide]Problem (Unofficial, please update when official one comes out):
is a polynomial with integer coefficients in the range, inclusive. There is exactly one integer such that . How many possible values are there for the ordered triple ?