计算6(7+1)(7^2+1)(7^4+1)……(7^32+1)

2024-11-28 02:41:20
推荐回答(1个)
回答(1):

这题利用了平方差公式。
原式=
(7-1)(7+1)(7^2+1)...(7^32+1)
=(7^2-1)(7^2+1)...(7^32+1)
=(7^4-1)(7^4+1)...(7^32+1)
=...
=(7^32-1)(7^32+1)
=7^64 - 1