DLMF:27.3.E8 (Q8009): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12093 / rank
 
Normal rank
Property / Symbols used: Q12093 / qualifier
 
Defining formula:

( m , n ) 𝑚 𝑛 {\displaystyle{\displaystyle\left(\NVar{m},\NVar{n}\right)}}

\pgcd{\NVar{m},\NVar{n}}
Property / Symbols used: Q12093 / qualifier
 
xml-id: C27.S1.p2.t1.r3.m6abdec
Property / Symbols used
 
Property / Symbols used: Q12239 / rank
 
Normal rank
Property / Symbols used: Q12239 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12239 / qualifier
 
xml-id: C27.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1gdec

Latest revision as of 14:15, 2 January 2020

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DLMF:27.3.E8
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    Statements

    ϕ ( m ) ϕ ( n ) = ϕ ( m n ) ϕ ( ( m , n ) ) / ( m , n ) . Euler-totient-phi 𝑚 Euler-totient-phi 𝑛 Euler-totient-phi 𝑚 𝑛 Euler-totient-phi 𝑚 𝑛 𝑚 𝑛 {\displaystyle{\displaystyle\phi\left(m\right)\phi\left(n\right)=\phi\left(mn% \right)\phi\left(\left(m,n\right)\right)/\left(m,n\right).}}
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    DLMF:27.3.E8
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    ϕ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    C27.S2.E7.m2aadec
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    ( m , n ) 𝑚 𝑛 {\displaystyle{\displaystyle\left(\NVar{m},\NVar{n}\right)}}
    C27.S1.p2.t1.r3.m6abdec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C27.S1.XMD3.m1bdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C27.S1.XMD4.m1gdec
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