9. (5 points) $1^{2013}+2^{2013}+3^{2013}+4^{2013}+5^{2013}$ divided by 5, the remainder is $\qquad$ . ( $a^{2013}$ represents 2013 $a$s multiplied together)
【Solution】Solution: The unit digit of the result of multiple 2s multiplied follows a pattern: $2, 4, 8, 6$ with every 4 twos multiplied forming a cycle. The unit digit of the result of multiple 3s multiplied follows a pattern: 3, 9, 7, 1 with every 4 threes multiplied forming a cycle,
$$
2013 \div 4=503 \cdots 1 \text {, }
$$

Therefore, the unit digit of 2013 twos multiplied is 2, the unit digit of 2013 threes multiplied is 3, the unit digit of 2013 fours multiplied is 4, 1 to any power is 1, and the unit digit of 5 to any power is $5,1+2+3+4+5=15$ so the unit digit of $1^{2013}+2^{2013}+3^{2013}+4^{2013}+5^{2013}$ is 5,

Therefore, the remainder when divided by 5 is 0;
The answer is: 0.