Regarding a certain problem of Korkin and Zolotarev

Abstract

Korkin and Zolotarev establish that the sought polynomials have n roots in the interval (-1, +1) and derive a series of equations that these roots satisfy; from the analysis of these equations, they deduce the uniqueness of the solution to the problem. This note proposes a simpler proof of the uniqueness of the solution, requiring only knowledge of the number of roots of the sought polynomials in the interval (-1, +1). The method of proof can be successfully applied to many similar problems of a more general nature.

Read more

None