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Hensel's lemma for polynomial rings

Source: Miklós Schweitzer 2016, Problem 3

November 2, 2016
algebrapolynomialRing TheoryField theoryMiklos Schweitzer

Problem Statement

Prove that for any polynomial PP with real coefficients, and for any positive integer nn, there exists a polynomial QQ with real coefficients such that P(x)2+Q(x)2P(x)^2 +Q(x)^2 is divisible by (1+x2)n(1+x^2)^n.
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