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Fungrim entry: dd9d26

Bn+p≡Bn+Bn+1(modp)B_{n + p} \equiv B_{n} + B_{n + 1} \pmod {p}
Assumptions:n∈Z≥0  and⁡  p∈Pn \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; p \in \mathbb{P}
TeX:
B_{n + p} \equiv B_{n} + B_{n + 1} \pmod {p}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; p \in \mathbb{P}
Definitions:
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
PPP\mathbb{P} Prime numbers
Source code for this entry:
Entry(ID("dd9d26"),
    Formula(CongruentMod(BellNumber(Add(n, p)), Add(BellNumber(n), BellNumber(Add(n, 1))), p)),
    Variables(n, p),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(p, PP))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC