如果一个四位自然数
的各数位上的数字均不为0,满足
,则称该四位数为“和百数”.例如:四位数3268,
,
3268是“和百数”;又如四位数4367,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
,
4367不是“和百数”.若一个“和百数”的前三个数字组成的三位数
与后三个数字组成的三位数
的和能被11整除,则满足条件的最大“和百数”与最小“和百数”的差是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ddb334f4736521eeb46b1d02cc7a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f826ebb0201c7a5996f068d6d7d48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf059956415ef20228fe325f16fee49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5920d60a755f43c8bccfc9ceb5613b12.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a675d752761f68640cb84085823063bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1d5c8b39ca4c7cbcf4175f5e235522.png)
23-24八年级下·重庆长寿·期中 查看更多[2]
更新时间:2024-05-20 18:49:12
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【推荐1】在正数范围内定义一种运算“△”,其规则是a△b=
,根据这一规则,方程x△(x+1)=
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【推荐2】对于各位数字均不为零的三位自然数
,若m满足各位数字之和能被十位数字整除,则称m为“对偶数”,例如
是“对偶数”;又如
不能被3整除,
不是“对偶数”,将m的百位数字放在其个位数字后得
,再将
的百位数字放在其个位数字后得
.记
.已知一个“对偶数”
(其中
),若
能被7整除,则所有满足条件的n的最大值为 ________ .
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【推荐1】已知m,n均为正整数,且满足
,则当m=___ 时,n取得最小值__ .
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【推荐2】如果一个三位数的十位数字等于它的百位和个位数字的差的绝对值,那么称这个三位数为“奇异数”,如:三位数
,∵
,∴
是“奇异数”,把一个奇异数m的任意一个数位上的数字去掉,得到三个两位数,这三个两位数之和记为
,把m的百位数字与个位数字之差的2倍记为
,则
的值为______ ;若三位数A是“奇异数”,且
是完全平方数,且百位数字小于个位数字,请求出所有符合条件的A的最大值为______ .
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