On a curious property of Bell numbers
Zhi-Wei Sun, Don Zagier
TL;DR
This paper explores a unique property of Bell numbers, deriving congruences that relate Bell numbers and derangement numbers modulo any prime, revealing new mathematical relationships.
Contribution
It introduces novel congruences connecting Bell numbers and derangement numbers modulo primes, expanding understanding of their number-theoretic properties.
Findings
Derived congruences between Bell and derangement numbers modulo primes
Established new relationships in number theory involving these combinatorial numbers
Enhanced mathematical understanding of Bell numbers' properties
Abstract
In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.
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Taxonomy
TopicsAdvanced Mathematical Identities · Benford’s Law and Fraud Detection · History and Theory of Mathematics