Kakeya's Problem on the Zeros of the Derivative of a Polynomial

1939 ◽  
Vol 45 (3) ◽  
pp. 355
Author(s):  
Morris Marden
Keyword(s):  
Derivative Of A Polynomial

scholarly journals The Schur Derivative of a Polynomial

1953 ◽  
Vol 1 (4) ◽  
pp. 159-163
Author(s):  
L. Carlitz
Keyword(s):  
Elementary Methods ◽  
Image Position ◽  
Derivative Of A Polynomial

For a given sequence {am} and p≠0, Schur (2) definedIn particular if p is a prime, a an integer and , then by Fermat's theoremis integral. Schur proved that if p † a, then all the derivativesare integral. Zorn (3) using p-adic methods proved Schur's results and also found the residue of Xm (mod pm), where and x = 1 (mod p). The writer (1) proved Zorn's congruences by elementary methods as well as certain additional results of a similar sort.

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