Exponents and mod (Euler's theorem) I know how to compute $7^{402} \pmod{10}$ using Euler's theorem since $7$ and $10$ are relatively prime.
But is there an easy way without using a calculator to compute $12^{720} \pmod{10}$. I don't think Euler's Theorem can be applied because $12$ and $10$ are not relatively prime...
Also, for $5^{1806} \pmod{63}$, finding $\varphi(63)$ is kinda difficult. Is there an easy way to solve that?

I would refer you to the modular exponentiation article on Wikipedia.
