Question

若A=(2+1)(22+1)(24+1)(28+1),则A-2003的末位数字是

Answer 1

a=(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1)
=2^16-1
2^n的末尾数字为2、4、8、6循环
所以2^16的末尾数字为6，所以2^16-1的末尾数字为5
所以A-2003的末尾数字为2

Answer 2

A=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1)
=2^16-1
=65536-1
=65535
那么A-2003=63532的个位数字是:2