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Duke Math Meet

Construction of polynomials

The polynomial P(x) has the property that P(1), P(2), P(3), P(4), and P(5) are equal to 1, 2, 3, 4, 5 in some order. How many possibilities are there for the polynomial P, given that the degree of P is strictly less than 4? (Duke Math Meet 2013 Tiebreaker round) Discussion: Let \(P(x) = a […]