You are here
Homeproof that Euler $\varphi$ function is multiplicative
Primary tabs
proof that Euler $\varphi$ function is multiplicative
Suppose that $t=mn$ where $m,n$ are coprime. The Chinese remainder theorem states that $\gcd(a,t)=1$ if and only if $\gcd(a,m)=1$ and $\gcd(a,n)=1$.

$\{a:a\equiv 1\;\;(\mathop{{\rm mod}}t)\}$

$\{a:a\equiv 1\;\;(\mathop{{\rm mod}}m)\text{ and }a\equiv 1\;\;(\mathop{{\rm mod% }}n)\}$
Related:
EulerPhiFunction, MultiplicativeFunction, EulerPhifunction
Type of Math Object:
Proof
Major Section:
Reference
Parent:
Mathematics Subject Classification
11A25 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
 Corrections