用简便方法计算:6 * (7+1) * (7^2 + 1) * (7^4 + 1) * (7^8 + 1) + 1

2024-11-27 21:49:48
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回答1:

6 * (7+1) * (7^2 + 1) * (7^4 + 1) * (7^8 + 1) + 1
=(7-1)*(7+1)*(7^2+1)*(7^4+1)*(7^8+1)+1
=(7^2-1)*(7^2+1)*(7^4+1)*(7^8+1)+1
=(7^4-1)*(7^4+1)*(7^8+1)+1
=(7^8-1)(7^8+1)+1
=(7^16-1)+1
=7^16