18的2011次方除以11的余数,快
问题描述：
18的2011次方除以11的余数,快
答
18的2011次方除以11的余数为7
因
2^5 = 32
32 | 11 = (-1) | 11
3^5 = 243
243 | 11 = 1 | 11 = 1
则
18^ 2011 | 11
= (2*3^2)^2011 | 11
= 2^2011 * 3^4022 | 11
= (2^5)^402 * 2 * (3^5)^804 * 3^2 | 11
= (-1)^402 * (1)^804 * 18 | 11
= 18 | 11
= 7