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ab≡{ab≡ϕ(m),[l]gcd(a,m)=1ab,[l]gcd(a,m)≠1, b<ϕ(m)a(bmod ϕ(m))+ϕ(m),[l]gcd(a,m)≠1, b≥ϕ(m)a^b \equiv \begin{cases} a^{b \equiv \phi(m)}, & \begin{aligned}[l] &\gcd(a,m)=1 \end{aligned} \\ a^b, & \begin{aligned}[l] &\gcd(a,m) \ne 1, \ b < \phi(m) \end{aligned} \\ a^{(b \mod \phi(m))+\phi(m)}, & \begin{aligned}[l] &\gcd(a,m) \ne 1, \ b \geq \phi(m) \end{aligned} \end{cases} ab≡⎩⎨⎧ab≡ϕ(m),ab,a(bmodϕ(m))+ϕ(m),[l]gcd(a,m)=1[l]gcd(a,m)=1, b<ϕ(m)[l]gcd(a,m)=1, b≥ϕ(m)
