MathDB
Both a and a+1997 are roots of P, Q(P(x))=1 has no solutions

Source: Baltic Way 1997

January 28, 2011
algebrapolynomialnumber theory proposednumber theory

Problem Statement

Let PP and QQ be polynomials with integer coefficients. Suppose that the integers aa and a+1997a+1997 are roots of PP, and that Q(1998)=2000Q(1998)=2000. Prove that the equation Q(P(x))=1Q(P(x))=1 has no integer solutions.
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