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Smallest degree

Author: mathforces
Problem has been solved: 8 times

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Let $P$ and $Q$ be nonzero polynomials with nonnegative real coefficients such that $$x^2 - \frac{1+\sqrt{3}}{\sqrt{2}} x + 1 = \frac{P(x)}{Q(x)}.$$ Find the smallest possible value of the degree of $P$.

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