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Fungrim entry: ff190c

(B2n+∑p∈P, (p−1)∣2n1p)∈Z\left(B_{2 n} + \sum_{p \in \mathbb{P},\,\left(p - 1\right) \mid 2 n} \frac{1}{p}\right) \in \mathbb{Z}
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
\left(B_{2 n} + \sum_{p \in \mathbb{P},\,\left(p - 1\right) \mid 2 n} \frac{1}{p}\right) \in \mathbb{Z}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
BernoulliBBnB_{n} Bernoulli number
PPP\mathbb{P} Prime numbers
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("ff190c"),
    Formula(Element(Parentheses(Add(BernoulliB(Mul(2, n)), SumCondition(Div(1, p), p, And(Element(p, PP), Divides(Parentheses(Sub(p, 1)), Mul(2, n)))))), ZZ)),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

Topics using this entry

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2019-06-18 07:49:59.356594 UTC