Question

试求（2-1）（2+1）（2²+1）（2的4次幂+1）…（2的32次幂+1）+1的个位数字.

Answer 1

(2-1)(2+1)(2^2+1)(2^4+1)...(2^32+1)+1

=(2^2-1)(2^2+1)(2^4+1)...(2^32+1)+1

=(2^4-1)(2^4+1)...(2^32+1)+1

=...

=2^64-1+1

=2^64

2^1=2

2^2=4

2^3=8

2^4=16

2^5=32

...

64/4=16

所以,2^64的个位数=2^4的个位数=6