On the Casas-Alvero conjecture (Q634493)

Summary: The Casas-Alvero conjecture says that a complex univariate polynomial having roots in common with each of its derivatives must be a power of a linear polynomial. In this expository note we review some ideas on this conjecture. In particular, we explain the rather successful algebraic attack by \textit{H.-C. Graf von Bothmer} et al. [J. Algebra 316, No. 1, 224--230 (2007; Zbl 1127.12002)], which proves the conjecture in infinitely many degrees, and challenge analysts to come up with new approaches.