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Fungrim entry: afd0c5

(χ ⁣(n)=0)    (gcd ⁣(n,q)1)\left(\chi\!\left(n\right) = 0\right) \iff \left(\gcd\!\left(n, q\right) \ne 1\right)
Assumptions:qZ1andχGqandnZq \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\left(\chi\!\left(n\right) = 0\right) \iff \left(\gcd\!\left(n, q\right) \ne 1\right)

q \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \chi \in G_{q} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
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("afd0c5"),
    Formula(Equivalent(Equal(chi(n), 0), Unequal(GCD(n, q), 1))),
    Variables(q, chi, n),
    Assumptions(And(Element(q, ZZGreaterEqual(1)), Element(chi, DirichletGroup(q)), Element(n, ZZ))))

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

2019-08-17 11:32:46.829430 UTC