Unfair 0–1 polynomial conjecture

Determine whether every factorization C(x)=A(x)B(x) of a monic polynomial C(x) with coefficients in {0,1}, where A(x) and B(x) are monic polynomials with nonnegative real coefficients, must be a factorization into polynomials whose coefficients all belong to {0,1}.

Background

The paper studies factorizations of monic 0–1 polynomials into monic factors with nonnegative real coefficients. The general conjecture asks whether allowing arbitrary nonnegative real coefficients in the factors can produce genuinely non-0–1 factors, or whether the coefficient restriction is automatically inherited by both factors.

The paper proves the conjecture only for the specific trinomial family 1+a x^2+x^k with 0<a<1 and odd k≥341, while describing the general problem as an open problem and noting that it remains substantially more difficult for factors with several delays and interacting packet families.