证明 四个连续奇数的乘积减去一,必能被八整除

设这四个奇数为 2n-3,2n-1,2n+1,2n+3
则他们的积减1为
(2n-3)(2n-1)(2n+1)(2n+3)-1
=(2n-3)(2n+3)(2n-1)(2n+1)-1
=(4n^2-9)(4n^2-1)-1
=16n^4-40n^2+8
=8(2n^4-5n^2+1)
所以四个连续奇数的乘积减去一,必能被八整除
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