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"d"ifferent values

Source: EGMO 2024 P6

April 14, 2024
algebrapolynomial

Problem Statement

Find all positive integers dd for which there exists a degree dd polynomial PP with real coefficients such that there are at most dd different values among P(0),P(1),P(2),⋯ ,P(d2−d)P(0),P(1),P(2),\cdots,P(d^2-d) .
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