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Part of 2013 Mediterranean Mathematics Olympiad

Problems(1)

Polynomial with nine distinct nonegative integer roots

Source: MMC 2013

Do there exist two real monic polynomials

P(x)

Q(x)

of degree 3,such that the roots of

P(Q(X))

are nine pairwise distinct nonnegative integers that add up to

72

? (In a monic polynomial of degree 3, the coefficient of

x^{3}

1

algebrapolynomialalgebra proposed