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(m)0 = 1, [m]t = (a™ - l)(a—» - 1) • • • (a»"**1 - 1), [m]0 = 1. In the following theorems p denotes an odd prime; the rational numbers a, u are integral (mod p) and p\a. We now state the following theorems.

A note on Bernoulli numbers and polynomials of higher order