Question

求(3-1)(3+1)(3²+1)(3³²+1)···(3³²+1)+1的个位数字是几

求(3-1)(3+1)(3²+1)（3⁴+1）···(3³²+1)+1的个位数字是几

Answer 1

21412414144

Answer 2

(3-1)(3+1)(3²+1)(3的4次方+1)···(3³²+1)+1
=(3²-1)(3²+1)(3的4次方+1)···(3³²+1)+1
=(3的4次方-1)(3的4次方+1)···(3³²+1)+1
=3的64次方-1+1
=3的64次方
∵3的4次方的个位数是1
∴3的64次方的个位数=（3的4次方)的16次方的个位数=1的64次方的个位数=1