作业帮求2^999的末两位数（不准找规律,用同余,幼儿园的孩子才找规律呢）
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/07/14 06:19:54
求2^999的末两位数（不准找规律,用同余,幼儿园的孩子才找规律呢）
2^999 | 100 以下等于号表同余
= 512^111
= (500+12)^111
= 12^111
= 1728^37
= 28^37
= 14^36 * 2^37 * 14
= 196^18* 2^37 * 14
= (200-4)^18 * 2^38 * 7
= 2^74 * 7
= 512^8 * 28
= 12^8 * 28
= 1728^2 *12*12*28
= 28^3 *12*12
= 7^3 * 2^10 * 3^2
= 7^3 * 2^3 * 3^3
= 74088
= 88
= 512^111
= (500+12)^111
= 12^111
= 1728^37
= 28^37
= 14^36 * 2^37 * 14
= 196^18* 2^37 * 14
= (200-4)^18 * 2^38 * 7
= 2^74 * 7
= 512^8 * 28
= 12^8 * 28
= 1728^2 *12*12*28
= 28^3 *12*12
= 7^3 * 2^10 * 3^2
= 7^3 * 2^3 * 3^3
= 74088
= 88