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?

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?
数学人气:406 ℃时间:2020-05-19 05:42:25
优质解答
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
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