Problem

Source: Polish Mathematical Olympiad 2016 P1- Final Round

Tags: algebra, polynomial, number theory, prime numbers, quadratics



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