已知31=3,32=9,33=27,34=81,35=243,36=729,37=2187,38=6561… 求(3-1)(3+1)(32+1)(34+1)•…•(332+1)+2的个位数字.

问题描述:

已知31=3,32=9,33=27,34=81,35=243,36=729,37=2187,38=6561…
求(3-1)(3+1)(32+1)(34+1)•…•(332+1)+2的个位数字.

原式=(3-1)(3+1)(32+1)(34+1)(38+1)(316+1)(332+1)+2=(32-1)(32+1)(34+1)(38+1)(316+1)(332+1)+2=(34-1)(34+1)(38+1)(316+1)(332+1)+2=(38-1)(38+1)(316+1)(332+1)+2=...