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Fungrim entry: 775e10

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

m \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Totientφ(n)\varphi(n) Euler totient function
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("775e10"),
    Formula(LessEqual(Mul(Totient(m), Totient(n)), Totient(Mul(m, n)))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZGreaterEqual(0)), Element(n, ZZGreaterEqual(0)))))

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2019-10-05 13:11:19.856591 UTC