Calculate $85^{2014}\bmod {82}$ Calculate the following equation $$85^{2014}\equiv x \bmod {82}$$
Answer is 73 in Wolphram Alpha, but I always lose myself doing the step by step

$$85\equiv3\pmod{82}\implies85^{2014}\equiv3^{2014}\pmod{82}$$
$$2014\equiv14\pmod{\phi(82)}\implies3^{2014}\equiv3^{14}\pmod{82}$$
Now $3^4\equiv-1\pmod{82}\implies3^{14}=3^2(3^4)^3\equiv9(-1)^3\pmod{82}\equiv ?$
