试确定3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^31+1)(2^64+1)+1的末位数字.
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3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2²-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2⁴-1)(2⁴+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^32-1)(2^32+1)(2^64+1)+1
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
∵2×2=4 4×4=16 16×16=256
∴3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^31+1)(2^64+1)+1的末位数字是6
=(2²-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2⁴-1)(2⁴+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^32-1)(2^32+1)(2^64+1)+1
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
∵2×2=4 4×4=16 16×16=256
∴3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^31+1)(2^64+1)+1的末位数字是6
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