Problem

Source: Czech-Polish-Slovak 2005 Q3

Tags: algebra, polynomial, modular arithmetic, quadratics, algebra unsolved



Find all integers $n \ge 3$ for which the polynomial \[W(x) = x^n - 3x^{n-1} + 2x^{n-2} + 6\] can be written as a product of two non-constant polynomials with integer coefficients.