MathDB
Beautiful polynomial problem

Source: Iranian National Olympiad (3rd Round) 2006

August 26, 2006
algebrapolynomialnumber theory proposednumber theory

Problem Statement

a) P(x),R(x)P(x),R(x) are polynomials with rational coefficients and P(x)P(x) is not the zero polynomial. Prove that there exist a non-zero polynomial Q(x)∈Q[x]Q(x)\in\mathbb Q[x] that P(x)∣Q(R(x)).P(x)\mid Q(R(x)). b) P,RP,R are polynomial with integer coefficients and PP is monic. Prove that there exist a monic polynomial Q(x)∈Z[x]Q(x)\in\mathbb Z[x] that P(x)∣Q(R(x)).P(x)\mid Q(R(x)).
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