Find the last $3$ digits of $3^{352}$? Find the last $3$ digits of $3^{352}$ ?
Apart from Carmichael Function, any other way of solving it ?

Note that $3^4=81$, so $$\begin{aligned}3^{352} &\equiv (80+1)^{88} \pmod{1000} \\ &\equiv 1+\binom{88}{1} 80 + \binom{88}{2} 6400\pmod{1000}
\\&\equiv 1+040+200 \pmod{1000}
\end{aligned}
$$
Because last two digits of $88\times 8$ is $04$, while last digit of $44\times 87\times 64$ is $2$.
