[tex]27\equiv 13\cdot 2 +1 \mod(13) \\~\\27 \equiv 1 \mod(13) \\~\\3^3 \equiv 1 \mod(13) \\~\\\left(3^3\right)^{66} \equiv \left(1\right)^{66} \mod(13) \\~\\3^{198} \equiv 1 \mod(13) \\~\\3^{198}\cdot 3^2 \equiv 1\cdot 9 \mod(13) \\~\\3^{200} \equiv 9 \mod(13)[/tex]
3^200 dá resto 9 na divisão por 13.
