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The Distinct Zeros of the Product of a Polynomial and its Successive Derivatives

Published online by Cambridge University Press:  20 November 2018

Q. I. Rahman
Q. I. Rahman*
Affiliation:
Université de Montréal, Montréal, Québec
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Extract

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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 267 - 269
Copyright
Copyright © Canadian Mathematical Society 1971