Abstract
Schur [6] proved that the derivatives AaP, l2a2m, . . . , A'P-aPm are all integral. If aP-1 1 (mod p2) then all the derivatives AraPr are integral, while if aP-1 * 1 (mod p2), then every number APOY has exactly the denominator p. A. Brauer [1] gave another proof of these results; about the same time Zorn [7] also proved these and other results by p-adic methods. In the present paper we consider sequences of rational numbers {am} that are integral (mod p), where p is a fixed prime. (More generally the a,m may be integral p-adic numbers.) Now suppose that the am satisfy
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