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(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1/4
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(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1/4
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答案和解析
(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)+1/4
=(5-1)(5+1) (5^2+1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1/4
=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)/4+1/4
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)/4+1/4
=(5^8-1)(5^8+1)(5^16+1)/4+1/4
=(5^16-1)(5^16+1)/4+1/4
=(5^32-1)/4+1/4
=5^32/4
=(5-1)(5+1) (5^2+1)(5^4+1)(5^8+1)(5^16+1)/(5-1)+1/4
=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)/4+1/4
=(5^4-1)(5^4+1)(5^8+1)(5^16+1)/4+1/4
=(5^8-1)(5^8+1)(5^16+1)/4+1/4
=(5^16-1)(5^16+1)/4+1/4
=(5^32-1)/4+1/4
=5^32/4
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