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Girls in Math at Yale 2022 Problem 9: Monic Quadratics Strike Again

Source:

February 27, 2022
Yalecollegequadratics

Problem Statement

Suppose that P(x)P(x) is a monic quadratic polynomial satisfying aP(a)=20P(20)=22P(22)aP(a) = 20P(20) = 22P(22) for some integer a≠20,22a\neq 20, 22. Find the minimum possible positive value of P(0)P(0).
Proposed by Andrew Wu
(Note: wording changed from original to specify that a≠20,22a \neq 20, 22.)
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