计算:(2加1)(2的平方加1)(2的4平方加1)……(2的32平方加1)加1
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(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=1×(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2-1)(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2²-1)(2²+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
=1×(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2-1)(2+1)(2²+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2²-1)(2²+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
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