Geodesic
The Distinct Zeros of the Product of a Polynomial and its Successive Derivatives
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 267-269

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It has been conjectured that if p(z) is a polynomial of degree n then the product P(z)=p(z)p'(z)p"(z)...p(n-1)(z) has at least n+1 distinct zeros unless p(z)=c(z—a)n . Professor P. Erdös who mentioned this problem in a lecture at the University of Montreal attributed it to Tiberiu Popoviciu. 
Rahman, Q. I. The Distinct Zeros of the Product of a Polynomial and its Successive Derivatives. Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 267-269. doi: 10.4153/CMB-1971-050-9
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