MathDB

Polynomial with nine distinct nonegative integer roots

Source: MMC 2013

June 1, 2013

algebrapolynomialalgebra proposed

Problem Statement

Do there exist two real monic polynomials

P(x)

and

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