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Fungrim entry: db4763

(gcd ⁣(m,n)=1)    (φ ⁣(mn)=φ ⁣(m)φ ⁣(n))\left(\gcd\!\left(m, n\right) = 1\right) \implies \left(\varphi\!\left(m n\right) = \varphi\!\left(m\right) \varphi\!\left(n\right)\right)
Assumptions:mZ0andnZ0m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
TeX:
\left(\gcd\!\left(m, n\right) = 1\right) \implies \left(\varphi\!\left(m n\right) = \varphi\!\left(m\right) \varphi\!\left(n\right)\right)

m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
GCDgcd ⁣(a,b)\gcd\!\left(a, b\right) Greatest common divisor
Totientφ ⁣(n)\varphi\!\left(n\right) Euler totient function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("db4763"),
    Formula(Implies(Equal(GCD(m, n), 1), Equal(Totient(Mul(m, n)), Mul(Totient(m), Totient(n))))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(0)))))

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2019-08-19 14:38:23.809000 UTC