试求(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的个位数字
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解:(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2²-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4+1)(2^4-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=(2^64-1)+1
=2^64
所以,计算结果的个位数是6.
=(2²-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4+1)(2^4-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=(2^64-1)+1
=2^64
所以,计算结果的个位数是6.
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原式=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4+1)(2^4-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=(2^64-1)+1
=2^64
=(2^4)^16
=16^16
个位永远是6*6*6*……
所以不用计算机可得出个位是6
=(2^4+1)(2^4-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=(2^64-1)+1
=2^64
=(2^4)^16
=16^16
个位永远是6*6*6*……
所以不用计算机可得出个位是6
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