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The Schur Derivative of a Polynomial
Published online by Cambridge University Press: 18 May 2009
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For a given sequence {am} and p≠0, Schur (2) defined
In particular if p is a prime, a an integer and , then by Fermat's theorem
is integral. Schur proved that if p † a, then all the derivatives
are 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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- Copyright © Glasgow Mathematical Journal Trust 1953