计算:8(7^2+1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)
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8(7^2+1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)
=(7-1)(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)/(7-1)
=(7^2-1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)/(7-1)
=(7^4-1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)/(7-1)
反复用平方差
=(7^64-1)/6
=(7-1)(7+1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)/(7-1)
=(7^2-1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)/(7-1)
=(7^4-1)(7^4+1)(7^8+1)(7^16+1)(7^32+1)/(7-1)
反复用平方差
=(7^64-1)/6
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