对于算式2(3+1)(32+1)(34+1)(38+1)(316+1)(332+1)+1的结果是几位数,个位是几?

问题描述:

对于算式2(3+1)(32+1)(34+1)(38+1)(316+1)(332+1)+1的结果是几位数,个位是几?

2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+1
=(3-1)(3+1)(3²+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+1
=(3²-1)(3²+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+1
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)+1
=(3^8-1)(3^8+1)(3^16+1)(3^32+1)+1
=(3^16-1)(3^16+1)(3^32+1)+1
=(3^32-1)(3^32+1)+1
=3^64-1+1
=3^64 =9^32=81^16个位是1