MathDB

1

Part of 2016 Polish MO Finals

Problems(1)

Polynomial

Source: Polish Mathematical Olympiad 2016 P1- Final Round

4/8/2016
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].
algebrapolynomialnumber theoryprime numbersquadratics