Question

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）

Answer 1

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