Prove that the product of any two consecutive odd numbers is 1 less than a multiple 4.
来源:百度知道 编辑:UC知道 时间:2024/05/31 05:54:46
英文好的帮帮忙~我不太理解这题的意思。翻译一下顺便做一下~是证明题。非常感谢~
题目翻译:证明任意2个连续奇数的乘积加1是4的倍数。
证明:设这两个奇数是2k-1,2k+1(k是任意整数),那么:
(2k-1)(2k+1)+1
=4k^2-1+1
=4k^2 是4的倍数
得证。
请证明任何两相邻的奇数的乘积都是四的倍数减去一。
或者:请证明任何两相邻奇数的乘积加上1之后都是4的倍数。
证明过程:
设a是不小于1的整数,
则:任何相邻的两奇数可以表示为2a-1和2a+1;
所以,任何两相邻奇数的乘积加上1以后可以表示为
(2a-1)*(2a+1)+1
=(4a^2-1)+1
=4a^2
于是:4a^2/4=a^2
由于a是不小于1的整数,故a^2也是不小于1的整数
即:任何两相邻奇数的乘积加上1之后都是4的倍数。
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