Abstract
The nth Bell number B n is the number of ways to partition a set of n elements into nonempty subsets. We generalize the “trace formula” of Barsky and Benzaghou [1], which asserts that for an odd prime p and an appropriate constant τ p , the relation B n = - Tr ( ϑ n - 1 - τ p ) B τ p holds in F p , where ϑ is a root of g ˜ ( x ) = x p - x - 1 and Tr : F p [ ϑ ] ⟶ F p is the trace form. We deduce some new interesting congruences for the Bell numbers, generalizing miscellaneous well-known results including those of Radoux [4].
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