有哪些日期是完全平方数？

nyy

比如2024年10月1日
20241001=4499的平方

northwolves

穷举即可：1600.01.01-3000.01.01 共90个日期是平方数

1. dd = Select[Range[4000, 5477], 100 < Mod[#^2, 10^4] < 1300 && 0 < Mod[#^2, 100] < 30 &]; {Length@dd, Table[{d^2, d}, {d, dd}]}

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{90,{{16120225,4015},{16200625,4025},{16281225,4035},{16370116,4046},{16410601,4051},{16851025,4105},{16900321,4111},{17181025,4145},{17230801,4151},{17430625,4175},{17850625,4225},{18071001,4251},{18190225,4265},{18361225,4285},{18931201,4351},{19140625,4375},{19351201,4399},{19580625,4425},{19820304,4452},{19900521,4461},{20151121,4489},{20241001,4499},{20720704,4552},{20930625,4575},{21150801,4599},{21390625,4625},{21520321,4639},{21641104,4652},{21650409,4653},{21790224,4668},{21921124,4682},{22071204,4698},{22080601,4699},{22231225,4715},{22420225,4735},{22591009,4753},{22600516,4754},{22800625,4775},{23011209,4797},{23020804,4798},{23030401,4799},{23280625,4825},{23571025,4855},{23961025,4895},{23970816,4896},{23980609,4897},{23990404,4898},{24000201,4899},{24651225,4965},{24681024,4968},{24730729,4973},{24750625,4975},{24770529,4977},{24820324,4982},{24850225,4985},{24890121,4989},{25110121,5011},{25150225,5015},{25180324,5018},{25230529,5023},{25250625,5025},{25270729,5027},{25321024,5032},{25351225,5035},{26020201,5101},{26030404,5102},{26040609,5103},{26050816,5104},{26061025,5105},{26471025,5145},{26780625,5175},{27050401,5201},{27060804,5202},{27071209,5203},{27300625,5225},{27520516,5246},{27531009,5247},{27720225,5265},{27931225,5285},{28100601,5301},{28111204,5302},{28281124,5318},{28430224,5332},{28590409,5347},{28601104,5348},{28740321,5361},{28890625,5375},{29170801,5401},{29430625,5425},{29680704,5448}}}

nyy

northwolves 发表于 2024-10-18 22:44
穷举即可：1600.01.01-3000.01.01 共90个日期是平方数

难道后两位不能是30、31？？？

nyy

你检查过不存在平年02月29这情况？？

northwolves

平方数后三位组合：
{000,001,004,009,016,024,025,036,041,044,049,056,064,076,081,084,089,096,100,104,116,121,124,129,136,144,156,161,164,169,176,184,196,201,204,209,216,224,225,236,241,244,249,256,264,276,281,284,289,296,304,316,321,324,329,336,344,356,361,364,369,376,384,396,400,401,404,409,416,424,436,441,444,449,456,464,476,481,484,489,496,500,504,516,521,524,529,536,544,556,561,564,569,576,584,596,600,601,604,609,616,624,625,636,641,644,649,656,664,676,681,684,689,696,704,716,721,724,729,736,744,756,761,764,769,776,784,796,801,804,809,816,824,836,841,844,849,856,864,876,881,884,889,896,900,904,916,921,924,929,936,944,956,961,964,969,976,984,996}

nyy

northwolves 发表于 2024-10-20 09:15
平方数后三位组合：
{000,001,004,009,016,024,025,036,041,044,049,056,064,076,081,084,089,096,100,104, ...

1. Clear["Global`*"];(*mathematica11.2,win7(64bit)Clear all variables*)
   
2. aa=Range[3163,9999]^2;(*生成所有可能的日期*)
   
3. bb=Select[aa,And[100<Mod[#,10^4]<1300,1<=Mod[#,100]<=31]&](*筛选出可能的日期,根据月份与日期*)
   
4. cc=Grid[Transpose[{bb}]](*复制成文本形式,然后用正则表达式查询229 30 31结尾的/229$\|30$\|31$ ,经检查没有*)
   
5. dd={#,Sqrt[#]}&/@Select[bb,Mod[#,10^4]==1001&](*中国*)
   
6. ee={#,Sqrt[#]}&/@Select[bb,Mod[#,10^4]==0704&](*美国*)
   

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搞出所有可能。只限制八位数日期。

1. {10080625,10220809,10310521,10400625,10491121,10660225,10791225,10870209,11390625,11580409,11730625,11930116,12271009,12581209,12630916,12680721,12730624,12780625,12830724,12880921,12931216,13140625,13300609,13490929,13520329,13660416,13801225,13860729,13890529,13950225,13980121,14250625,14470416,14630625,14830201,14861025,15000129,15031129,15171025,15241216,15350724,15460624,15570916,15610401,15721225,15800625,15880225,16120225,16200625,16281225,16370116,16410601,16851025,16900321,17181025,17230801,17430625,17850625,18071001,18190225,18361225,18931201,19140625,19351201,19580625,19820304,19900521,20151121,20241001,20720704,20930625,21150801,21390625,21520321,21641104,21650409,21790224,21921124,22071204,22080601,22231225,22420225,22591009,22600516,22800625,23011209,23020804,23030401,23280625,23571025,23961025,23970816,23980609,23990404,24000201,24651225,24681024,24730729,24750625,24770529,24820324,24850225,24890121,25110121,25150225,25180324,25230529,25250625,25270729,25321024,25351225,26020201,26030404,26040609,26050816,26061025,26471025,26780625,27050401,27060804,27071209,27300625,27520516,27531009,27720225,27931225,28100601,28111204,28281124,28430224,28590409,28601104,28740321,28890625,29170801,29430625,29680704,30261001,30371121,30680521,30780304,31080625,31371201,31640625,31911201,32661225,32890225,33051001,33350625,33930625,34210801,34281025,34680321,34751025,35390601,35450116,35581225,35700625,35820225,36180225,36300625,36421225,36590401,36650916,36820624,36990724,37161216,37271025,37491129,37540129,37761025,37810201,38130625,38390416,38750625,39200121,39250225,39350529,39400729,39501225,39740416,39980329,40030929,40360609,40640625,41011216,41100921,41190724,41280625,41370624,41460721,41550916,41641209,42211009,42850116,43230625,43520409,43890625,44930209,45091225,45360225,45711121,45900625,46090521,46280809,46580625,46991025,47541025,48260809,48330304,48511225,48650625,48790225,49210225,49350625,49491225,49660209,49730704,50481025,51051025,51151104,51380224,51480625,51581124,51811204,52200625,52620516,52780225,53071225,53260804,53450721,53860921,54361129,54390625,54420129,54700816,54730404,55100929,55130625,55160329,55771024,55980324,56520324,56731024,57350329,57380625,57410929,57790404,57820816,58110129,58140625,58171129,58690921,59120721,59320804,59521225,59830225,60000516,60450625,60871204,61121124,61230625,61340224,61591104,61701025,62331025,63170704,63250209,63441225,63600625,63760225,64240225,64400625,64561225,64770304,64850809,65691025,66341025,66830625,67190809,67420521,67650625,67881121,68310225,68641225,68840209,70140625,70610409,70980625,71470116,72301009,73051209,73170916,73290721,73410624,73530625,73650724,73770921,73891216,74390625,74770609,75220929,75290329,75620416,75951225,76090729,76160529,76300225,76370121,77000625,77510416,77880625,78340201,78411025,78730129,78801129,79121025,79281216,79530724,79780624,80030916,80120401,80371225,80550625,80730225,81270225,81450625,81631225,81830116,81920601,82901025,83010321,83631025,83740801,84180625,85100625,85581001,85840225,86211225,87441201,87890625,88341201,88830625,89340304,89510521,90041121,90231001,91240704,91680625,92140801,92640625,92910321,93161104,93180409,93470224,93741124,94051204,94070601,94381225,94770225,95121009,95140516,95550625,95981209,96000804,96020401,96530625,97121025,97911025,97930816,97950609,97970404,97990201,99301225,99361024,99460729,99500625,99540529,99640324,99700225,99780121}

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381个

中国国庆日的类型
{{18071001, 4251}, {20241001, 4499}, {30261001, 5501}, {33051001,
  5749}, {85581001, 9251}, {90231001, 9499}}

美帝国庆日
{{20720704, 4552}, {29680704, 5448}, {49730704, 7052}, {63170704,
  7948}, {91240704, 9552}}

美帝的比中国的少

nyy

northwolves 发表于 2024-10-20 09:15
平方数后三位组合：
{000,001,004,009,016,024,025,036,041,044,049,056,064,076,081,084,089,096,100,104, ...

1. Union[Mod[#^2,10^2]&/@Range[1,100]] (*穷举整数平方的后2位*)
   
2. Union[Mod[#^2,10^3]&/@Range[1,1000]](*穷举整数平方的后3位*)
   

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得到后两位
{0,1,4,9,16,21,24,25,29,36,41,44,49,56,61,64,69,76,81,84,89,96}
这个结果表明，后两位不存在30 31的情况

{0, 1, 4, 9, 16, 24, 25, 36, 41, 44, 49, 56, 64, 76, 81, 84, 89, 96, \
100, 104, 116, 121, 124, 129, 136, 144, 156, 161, 164, 169, 176, 184, \
196, 201, 204, 209, 216, 224, 225, 236, 241, 244, 249, 256, 264, 276, \
281, 284, 289, 296, 304, 316, 321, 324, 329, 336, 344, 356, 361, 364, \
369, 376, 384, 396, 400, 401, 404, 409, 416, 424, 436, 441, 444, 449, \
456, 464, 476, 481, 484, 489, 496, 500, 504, 516, 521, 524, 529, 536, \
544, 556, 561, 564, 569, 576, 584, 596, 600, 601, 604, 609, 616, 624, \
625, 636, 641, 644, 649, 656, 664, 676, 681, 684, 689, 696, 704, 716, \
721, 724, 729, 736, 744, 756, 761, 764, 769, 776, 784, 796, 801, 804, \
809, 816, 824, 836, 841, 844, 849, 856, 864, 876, 881, 884, 889, 896, \
900, 904, 916, 921, 924, 929, 936, 944, 956, 961, 964, 969, 976, 984, \
996}

这个结果表明，结尾不存在229的情况

northwolves

1600.01.01-3000.01.01 共2个日期是立方数：     {2, {{20570824, 274}, {27270901, 301}}}

nyy

northwolves 发表于 2024-10-21 22:55
1600.01.01-3000.01.01 共2个日期是立方数：     {2, {{20570824, 274}, {27270901, 301}}}

立方数的

1. Clear["Global`*"];(*mathematica11.2,win7(64bit)Clear all variables*)
   
2. pow=3;(*整数的多少次幂*)
   
3. aa=Range[IntegerPart[10^(7/pow)],IntegerPart[10^(8/pow)]]^pow;(*生成所有可能的8位数日期*)
   
4. bb=Select[aa,And[100<Mod[#,10^4]<1300,1<=Mod[#,100]<=31]&](*筛选出可能的日期,根据月份与日期*)
   
5. cc={#,#^(1/pow)}&/@bb(*日期与开根号的数*)
   
6. Grid[cc,Alignment->Left](*列表显示*)
   
7. dd=Select[cc,Mod[#[[1]],100]>=29&](*选出日期数>=29的,因为这个可能错误,人工核算一下*)
   

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输出结果
{{11390625,225},{20570824,274},{27270901,301},{30080231,311},{57960603,387},{64481201,401},{65450827,403},{66430125,405},{88121125,445},{98611128,462}}

第二列立方根
\[\begin{array}{ll}
11390625 & 225 \\
20570824 & 274 \\
27270901 & 301 \\
30080231 & 311 \\
57960603 & 387 \\
64481201 & 401 \\
65450827 & 403 \\
66430125 & 405 \\
88121125 & 445 \\
98611128 & 462 \\
\end{array}\]

nyy

nyy 发表于 2024-10-22 11:47
立方数的

四次方的结果

1. Clear["Global`*"];(*mathematica11.2,win7(64bit)Clear all variables*)
   
2. pow=4;(*整数的多少次幂*)
   
3. aa=Range[IntegerPart[10^(7/pow)],IntegerPart[10^(8/pow)]]^pow;(*生成所有可能的8位数日期*)
   
4. bb=Select[aa,And[100<Mod[#,10^4]<1300,1<=Mod[#,100]<=31]&](*筛选出可能的日期,根据月份与日期*)
   
5. cc={#,#^(1/pow)}&/@bb(*日期与开根号的数*)
   
6. Grid[cc,Alignment->Left](*列表显示*)
   
7. dd=Select[cc,Mod[#[[1]],100]>=29&](*选出日期数>=29的,因为这个可能错误,人工核算一下*)
   

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输出结果
{{17850625, 65}, {20151121, 67}, {31640625, 75}, {52200625,
  85}, {54700816, 86}, {81450625, 95}}
列表
\[\begin{array}{ll}
17850625 & 65 \\
20151121 & 67 \\
31640625 & 75 \\
52200625 & 85 \\
54700816 & 86 \\
81450625 & 95 \\
\end{array}\]