Question

(2+1)(2^2+1)(2^4+1).(2^512+1)的末尾数字是多少

Answer 1

(2+1)(2^2+1)(2^4+1)...(2^512+1)

=(2-1)(2+1)(2^2+1)(2^4+1)...(2^512+1)

=(2^2-1)(2^2+1).(2^512+1)

=...

=(2^512-1)(2^512+1)

=(2^1024-1)

2^1=2

2^2=4

2^3=8

2^4个位数是6

2^5个位数是2

所以个位数是4个一循环

1024/4=256

所以2^1024的个位数=2^4的个位数=6

即：2^1024-1的个位上是：6-1=5