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Do there exist polynomials ?

Source: 32-th Vietnamese Mathematical Olympiad 1994

February 24, 2007

algebrapolynomialalgebra unsolved

Problem Statement

Do there exist polynomials

p(x), q(x), r(x)

whose coefficients are positive integers such that

p(x) = (x^{2}-3x+3) q(x)

and

q(x) = (\frac{x^{2}}{20}-\frac{x}{15}+\frac{1}{12}) r(x)