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Algebra Difficulty 5.1 AIME, harder Prove it Belarus
Consider all polynomials P(x) with real coefficients that have the following property: for all real x and y one has
∣y2−P(x)∣≤2x⟺∣x2−P(y)∣≤2∣y∣.
Determine all possible values of P(0).
Solution
3. See IMO-2014 Shortlist, Problem A5.
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Source: MathNet,
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