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Fungrim entry: 0851cf

χ ⁣(mn)=χ(m)χ(n)\chi\!\left(m n\right) = \chi(m) \chi(n)
Assumptions:qZ1andχGqandmZandnZq \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q} \,\mathbin{\operatorname{and}}\, m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\chi\!\left(m n\right) = \chi(m) \chi(n)

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q} \,\mathbin{\operatorname{and}}\, m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
DirichletGroupGqG_{q} Dirichlet characters with given modulus
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("0851cf"),
    Formula(Equal(chi(Mul(m, n)), Mul(chi(m), chi(n)))),
    Variables(q, chi, m, n),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)), Element(m, ZZ), Element(n, ZZ))))

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2019-10-05 13:11:19.856591 UTC