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Polynomial

Source: Bulgarian TST1/2006 Problem 2

May 31, 2006
algebrapolynomialalgebra unsolved

Problem Statement

Find all couples of polynomials (P,Q)(P,Q) with real coefficients, such that for infinitely many x∈Rx\in\mathbb R the condition P(x)Q(x)−P(x+1)Q(x+1)=1x(x+2) \frac{P(x)}{Q(x)}-\frac{P(x+1)}{Q(x+1)}=\frac{1}{x(x+2)} Holds. Nikolai Nikolov, Oleg Mushkarov
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