Hard to Detect Factors of Univariate Integer Polynomials

We investigate the computational complexity of deciding whether a given univariate integer polynomial p(x) has factor q(x) satisfying specific additional constraints. When only constraint imposed on is to have degree smaller than and greater zero, problem equivalent testing irreducibility then it solvable in time. prove that monic factors properties NP-complete strong sense. In particular, any constant value k∈Z, we sense detect existence returns prescribed when evaluated at x=k (Theorem 1) or pair factors—whose product equal original polynomial—that return same 2). The list all investigated this paper reported end Section 1.