# Fungrim entry: a4d6fc

$B_{n + a} \equiv B_{n} \pmod {m}\; \text{ where } a = \begin{cases} 3, & m = 2\\13, & m = 3\\12, & m = 4\\781, & m = 5\\39, & m = 6\\ \end{cases}$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; m \in \{2, 3, \ldots, 6\}$
TeX:
B_{n + a} \equiv B_{n} \pmod {m}\; \text{ where } a = \begin{cases} 3, & m = 2\\13, & m = 3\\12, & m = 4\\781, & m = 5\\39, & m = 6\\ \end{cases}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; m \in \{2, 3, \ldots, 6\}
Definitions:
Fungrim symbol Notation Short description
BellNumber$B_{n}$ Bell number
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
Source code for this entry:
Entry(ID("a4d6fc"),
Formula(Where(CongruentMod(BellNumber(Add(n, a)), BellNumber(n), m), Equal(a, Cases(Tuple(3, Equal(m, 2)), Tuple(13, Equal(m, 3)), Tuple(12, Equal(m, 4)), Tuple(781, Equal(m, 5)), Tuple(39, Equal(m, 6)))))),
Variables(n, m),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(m, Range(2, 6)))))

## Topics using this entry

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