Geodesic
The Schur Derivative of a Polynomial
Glasgow mathematical journal, Tome 1 (1953) no. 4, pp. 159-163

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Carlitz, L. The Schur Derivative of a Polynomial. Glasgow mathematical journal, Tome 1 (1953) no. 4, pp. 159-163. doi: 10.1017/S204061850003567X
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[(1)] (1)Carlitz., L., “Some theorems on the Schur derivative,” Pacific Journal of Mathematics, vol. 3 (1953), pp. 321–332. Google Scholar | DOI

[(2)] (2)Schur, I., “Ein Beitrag zur elementaren Zahlentheorie,” Sitzungaberichte der Preussischen Akademie der Wissenschaften (1933), pp. 145–151. Google Scholar

[(3)] (3)Zorn, M., “p-adic analysis and elementary number theory,” Annals of Mathematics (2) vol. 38 (1937), pp. 451–464. Google Scholar | DOI

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