Question

4.3的八次方减去4的六次方能被17整除吗?为什么?

Answer 1

3^8-4^6

= (3^2)^4 - 2^12

= 9^4 - (2^3)^4

= 9^4 - 8^4

= (9^2+8^2)(9+8)(9-8)

= (9^2+8^2)*17

可以被17整除