对于一个三位自然数
,将各个数位上的数字分别3倍后取个位数字,得到三个新的数字
,
,
,我们对自然数
规定一个运算:
,例如:
,其各个数位上的数字分别3倍后再取个位数字分别是:3,9,8,则
.若已知两个三位数
,
(
,
为整数,且
,
),若
能被17整除,则
的最大值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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更新时间:2024-02-27 08:44:41
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【推荐1】各数位上的数字均不相等的两位数称为好数,
是由两个好数组成的有序数对,将
的各位数字中最大的数作为千位数字,将
的各位数字中最小的数作为百位数字,将
的各位数字中最小的数作为十位数字,将
的各位数字中最大的数作为个位数字,这样构成了一个新的四位数
,称为
的衍生数,若此时
(其中
,
,
,
为整数,
,
,
,
),记
.则
的衍生数为______ ;若
的衍生数为
,
的衍生数为
,其中
,
(
、
为整数,
,
,
),且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff6d838c156e98b50813db582fcf7aac.png)
______ .
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【推荐2】对于一个三位自然数
,将各个数位上的数字分别3倍后取个位数字,得到三个新的数字
,
,
,我们对自然数
规定一个运算:
,例如:
,其各个数位上的数字分别3倍后再取个位数字分别是:3,9,8,则
.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0c0a9e4c089d7af3b2788f9ce62bd1.png)
______ ;若已知两个三位数
,
(
,
为整数,且
,
),若
能被17整除,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abcfd7b4d0a18d7d36f854e8d1ebe6c.png)
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【推荐2】对于一个四位正整数,若千位数字是十位数字的2倍,百位数字比个位数字小2,那么称这个数M为“强基数”,例如:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
,
,
4325是个“强基数”;又如
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
,
6538不是一个“强基数”.若将任意一个四位正整数N的四位数字从个位到千位依次逆序排列得到一个新的四位数,那么称这个数为数N的“逆袭数”,同时记
为四位正整数N与其“逆袭数”之差,例如:
,其“逆袭数”为6785,
.若一个“强基数”M的个位数字为x,设
,且
是8的倍数,则所有满足题意的四位正整数M之和是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2902f5083d831282df11b4661e135b9e.png)
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