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Find all p(x) = x^2+ax+b such that p(x) | x^{2n} + ax^n + b

Source: Austrian Mathematical Olympiad 1997, Part 2, D2, P3

July 4, 2011
algebrapolynomialalgebra proposed

Problem Statement

For every natural number nn, find all polynomials x2+ax+bx^2+ax+b, where a2≥4ba^2 \geq 4b, that divide x2n+axn+bx^{2n} + ax^n + b.
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