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Polynomial

Source: Polish Mathematical Olympiad 2016 P1- Final Round

April 8, 2016
algebrapolynomialnumber theoryprime numbersquadratics

Problem Statement

Let pp be a certain prime number. Find all non-negative integers nn for which polynomial P(x)=x4−2(n+p)x2+(n−p)2P(x)=x^4-2(n+p)x^2+(n-p)^2 may be rewritten as product of two quadratic polynomials P1, P2∈Z[X]P_1, \ P_2 \in \mathbb{Z}[X].
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