Visibility density for polynomials with multiple distinct roots

Determine whether the visibility density satisfies D(F)=1 for every polynomial F in Z[x] with at least two distinct roots.

Background

The paper studies lattice-point visibility along polynomial lines of sight. For a polynomial F, the visibility density D(F) is the limiting proportion of lattice points that are visible along F, when this limit exists.

The authors previously formulated a conjecture asserting that every integer polynomial with at least two distinct roots has visibility density one. The present paper verifies sharp bounds for the special family F(x)=f(x)^m when f is quadratic, but does not resolve the conjecture for all polynomials with at least two distinct roots.