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Fungrim entry: afd0c5

(χ(n)=0)  ⟺  (gcd⁡ ⁣(n,q)≠1)\left(\chi(n) = 0\right) \iff \left(\gcd\!\left(n, q\right) \ne 1\right)
Assumptions:q∈Z≥1  and⁡  χ∈Gq  and⁡  n∈Zq \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \chi \in G_{q} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
TeX:
\left(\chi(n) = 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
ZZGreaterEqualZ≥n\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), NotEqual(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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2021-03-15 19:12:00.328586 UTC