Problem of the Week 1208
A Little Path
For a polynomial
Extra credit: Suppose P(f) ends up at the origin. Prove that f is divisible by
Extra credit (unsolved): For which polynomials f is P(f) a simple closed polygon, i.e., no overlap in the edges?
Source: Dan Kalman and Mark Verdi, Polynomials with closed Lill paths, Mathematics Magazine 88 (2015) 3-10. The paths are called Lill paths, hence the title of the problem.