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p,q

Source: Iran 2005

August 29, 2005
algebrapolynomialnumber theory proposednumber theory

Problem Statement

p(x)p(x) is an irreducible polynomial in Q[x]\mathbb Q[x] that \mbox{deg}\ p is odd. q(x),r(x)q(x),r(x) are polynomials with rational coefficients that p(x)∣q(x)2+q(x).r(x)+r(x)2p(x)|q(x)^2+q(x).r(x)+r(x)^2. Prove that p(x)2∣q(x)2+q(x).r(x)+r(x)2p(x)^2|q(x)^2+q(x).r(x)+r(x)^2
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