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[讨论] 把正整数n倒过来写得到N,N/n不是无限小数

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发表于 2020-6-13 19:41:16 | 显示全部楼层 |阅读模式

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不考虑\(n\)的末位为0的情况。以下几种是显然的:
(1)n是回文数。
(2)n是1089、2178及其衍生。
(3)n是2的幂或者5的幂。
其他的呢?
我用excel试了下,81/18,21/12,51/15,42/24……等等。越大似乎越少了,做到的最大的是57831/13875。
有什么规律吗?
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-6-13 19:48:52 | 显示全部楼层
2的幂,5的幂再乘以3,9或11显然也都可以。
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-6-15 10:30:31 | 显示全部楼层
暴力
  1. ParallelCombine[Select[#,({#,#//IntegerDigits}//Which[#[[-1,-1]]==0,False,(#[[2]]//Reverse)==#[[2]],False,(#[[2]]//Reverse//FromDigits)/#[[1]]//Denominator//FactorInteger//#[[All,1]]&//Complement[#,{1,2,5}]&//#!={}&,False,True,True]&)&]&,Range[10^8]]
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毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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