Dubickas–Sha squarefree distance-two conjecture for integer polynomials

Let f(x)Z[x]f(x)\in\mathbb{Z}[x] have degree n0n\geq 0. A polynomial is squarefree if it is not divisible by the square of an irreducible polynomial over Q\mathbb{Q}. Define L(fg)=j=0nbjajL(f-g)=\sum_{j=0}^{n}|b_j-a_j| when f(x)=j=0najxjf(x)=\sum_{j=0}^{n}a_jx^j and g(x)=j=0nbjxjg(x)=\sum_{j=0}^{n}b_jx^j. Dubickas–Sha squarefree distance-two conjecture. There is a squarefree polynomial g(x)Z[x]g(x)\in\mathbb{Z}[x] of degree at most nn satisfying

L(fg)2.L(f-g)\leq 2.

This conjecture is the squarefree-polynomial variant investigated by Dubickas and Sha. The supplied text does not state whether it has been resolved.

Sources & referencesView supporting material

Primary source

Michael Filaseta and Richard A. Moy, “The Distance to a Squarefree Polynomial Over F_2[x]”, arXiv:1906.07904 (2019).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.