几个vb小程序

ysr

3707=343+3364
3707=3364+343

1784=784+
1000
1784=
1000+784

ysr

借助程序终于把这个数拆分成了幂的和：
18591=14884+3707=14884+343+3364=122^2+7^3+58^2
18591=16807+1784=16807+1000+784=7^5+10^3+28^2

ysr

总之，经过验证，20000以内李明波幂和猜想是成立的，这是基础理论，容易理解。
我相信这是个有价值的定理，希望能得到重视研究证明和推广普及！

就是说除了如下13个数都可以表示（表示为不超过3个幂的和）：
7，15，23，87，111，119，167，335，1391，1455，1607，1679，1991.

且指数为大于等于2的素数。

ysr

李明波幂和猜想如上图所示：

ysr

求完美长方体的解：（条件放宽了一些，下面的解中不知道是否有符合标准的）
200000内解有14项解=/7758126551,22128600000,22128600000,23449167694,31294566236.3293,23449167694,32241873449
解=/7646788975,22229000000,22229000000,23507484396,31436553277.9915,23507484396,32353211025
解=/7622547484,22250800000,22250800000,23520232371,31467383133.6513,23520232371,32377452516
解=/3405149959,25764200000,25764200000,25988248265,36436081063.6929,25988248265,36594850041
解=/2755582876,26263600000,26263600000,26407762532,37142339316.742,26407762532,37244417124
解=/2516813824,26444800000,26444800000,26564295565,37398594814.244,26564295565,37483186176
解=/1070642944,27516800000,27516800000,27537620786,38914631753.108,27537620786,38929357056
解=/-1232278369,29142600000,29142600000,29168641462,41213860162.8142,29168641462,41232278369
解=/-5621124356,32013200000,32013200000,32502953916,45273501614.9624,32502953916,45621124356
解=/-5812599569,32132600000,32132600000,32654100761,45442358714.3097,32654100761,45812599569
解=/-6311435264,32441600000,32441600000,33049835486,45879350705.083,33049835486,46311435264
解=/-9799390625,34525000000,34525000000,35888768182,48825723240.9311,35888768182,49799390625
解=/-10928146496,35172800000,35172800000,36831375832,49741850786.6364,36831375832,50928146496
解=/-16919316736,38428800000,38428800000,41988521625,54346530145.7232,41988521625,56919316736

没有符合的，e都是小数，a有的是负数了

ysr

200000~300000之间解有65组解=/33886732400,85896000000,85896000000,92338688797,121475288153.599,92338688797,126113267600
解=/32728978439,86967600000,86967600000,92922276551,122990759407.038,92922276551,127271021561
解=/31038702016,88508800000,88508800000,93793436339,125170345349.368,93793436339,128961297984
解=/30092440000,89360000000,89360000000,94290850803,126374123933.66,94290850803,129907560000
解=/29894311351,89537200000,89537200000,94395868739,126624722576.912,94395868739,130105688649
解=/19533190000,98360000000,98360000000,100280781367,139102045995.018,100280781367,140466810000
解=/19138616599,98680400000,98680400000,100519192145,139555160020.402,100519192145,140861383401
解=/18838753136,98923200000,98923200000,100701033351,139898531073.346,100701033351,141161246864
解=/17053204336,100356800000,100356800000,101795378502,141925947636.364,101795378502,142946795664
解=/16295754391,100958800000,100958800000,102265492267,142777304200.913,102265492267,143704245609
解=/16245264991,100998800000,100998800000,102296951255,142833872743.408,102296951255,143754735009
解=/16070417351,101137200000,101137200000,102406013191,143029599900.44,102406013191,143929582649
解=/15764111296,101379200000,101379200000,102597511654,143371839582.534,102597511654,144235888704
解=/14870918384,102081600000,102081600000,103159087201,144365183188.745,103159087201,145129081616
解=/14173887644,102626400000,102626400000,103600564998,145135646737.526,103600564998,145826112356
解=/13720527296,102979200000,102979200000,103889212635,145634581282.331,103889212635,146279472704
解=/13620599836,103056800000,103056800000,103952993060,145744324254.772,103952993060,146379400164
解=/12905531324,103610400000,103610400000,104411051747,146527232882.901,104411051747,147094468676
解=/12896206064,103617600000,103617600000,104417044397,146537415220.55,104417044397,147103793936
解=/11080099324,105010400000,105010400000,105593336481,148507131870.224,105593336481,148919900676
解=/11022331504,105054400000,105054400000,105631050128,148569357266.968,105631050128,148977668496
解=/10067255296,105779200000,105779200000,106257182260,149594379256.976,106257182260,149932744704
解=/9876193519,105923600000,105923600000,106383026068,149798591695.383,106383026068,150123806481
解=/9841764124,105949600000,105949600000,106405723818,149835361248.004,106405723818,150158235876
解=/8697115324,106810400000,106810400000,107163899533,151052716282.495,107163899533,151302884676
解=/8544829279,106924400000,106924400000,107265285264,151213936628.606,107265285264,151455170721
解=/6908714684,108141600000,108141600000,108362059731,152935317376.726,108362059731,153091285316
解=/6884380799,108159600000,108159600000,108378474667,152960773220.849,108378474667,153115619201
解=/6861124636,108176800000,108176800000,108394165385,152985097694.122,108394165385,153138875364
解=/6318697751,108577200000,108577200000,108760904286,153551348804.496,108760904286,153681302249
解=/6256795751,108622800000,108622800000,108802850022,153615836942.94,108802850022,153743204249
解=/6228007900,108644000000,108644000000,108822363595,153645818270.463,108822363595,153771992100
解=/6097577500,108740000000,108740000000,108910826144,153781582772.45,108910826144,153902422500
解=/5469361991,109201200000,109201200000,109338081207,154433818067.417,109338081207,154530638009
解=/5250252784,109361600000,109361600000,109487555041,154660657922.821,109487555041,154749747216
解=/4752378031,109725200000,109725200000,109828068416,155174865974.1,109828068416,155247621969
解=/4508041436,109903200000,109903200000,109995617221,155426595988.203,109995617221,155491958564
解=/4282571776,110067200000,110067200000,110150483144,155658527012.432,110150483144,155717428224
解=/3724055239,110472400000,110472400000,110535151645,156231566347.906,110535151645,156275944761
解=/3579267751,110577200000,110577200000,110635113402,156379775929.242,110635113402,156420732249
解=/3117465271,110910800000,110910800000,110954603989,156851557573.65,110954603989,156882534729
解=/2228734375,111550000000,111550000000,111572262489,157755522882.719,111572262489,157771265625
解=/1293380791,112218800000,112218800000,112226253200,158701348913.234,112226253200,158706619209
解=/936682876,112472800000,112472800000,112476700319,159060559158.077,112476700319,159063317124
解=/444976975,112822000000,112822000000,112822877505,159554402534.057,112822877505,159555023025
解=/-966426116,113818400000,113818400000,113822502863,160963524927.606,113822502863,160966426116
解=/-1078576049,113897200000,113897200000,113902306799,161074964956.321,113902306799,161078576049
解=/-2271448900,114732000000,114732000000,114754482719,162255550438.19,114754482719,162271448900
解=/-2536118681,114916400000,114916400000,114944381711,162516331419.092,114944381711,162536118681
解=/-3677132900,115708000000,115708000000,115766413827,163635822875.066,115766413827,163677132900
解=/-4929113476,116570400000,116570400000,116674565848,164855440651.257,116674565848,164929113476
解=/-5254656256,116793600000,116793600000,116911746259,165171093118.378,116911746259,165254656256
解=/-5643437201,117059600000,117059600000,117195555955,165547273925.97,117195555955,165643437201
解=/-5653972889,117066800000,117066800000,117203255380,165557456263.619,117203255380,165653972889
解=/-5774008384,117148800000,117148800000,117291007815,165673421775.733,117291007815,165774008384
解=/-6785624836,117837600000,117837600000,118032811871,166647532077.496,118032811871,166785624836
解=/-7544382641,118351600000,118351600000,118591816463,167374437848.556,118591816463,167544382641
解=/-8156141921,118764400000,118764400000,119044131978,167958225207.103,119044131978,168156141921
解=/-8533622116,119018400000,119018400000,119323938273,168317435451.946,119323938273,168533622116
解=/-8925029209,119281200000,119281200000,119614634639,168689090776.138,119614634639,168925029209
解=/-9138073600,119424000000,119424000000,119773102845,168891040472.845,119773102845,169138073600
解=/-9327461129,119550800000,119550800000,119914116399,169070362752.553,119914116399,169327461129
解=/-9411764324,119607200000,119607200000,119976929447,169150124397.471,119976929447,169411764324
解=/-9676291600,119784000000,119784000000,120174195546,169400157355.299,120174195546,169676291600
解=/-9986800484,119991200000,119991200000,120406080666,169693182405.423,120406080666,169986800484

朋友的公式，我仅仅验证一下而已（负数可以取绝对值）

ysr

300000~400000之间解有96组解=/88375131584,181617600000,181617600000,201978009972,256846073085.652,201978009972,271624868416
解=/88336382400,181656000000,181656000000,201995591020,256900378886.447,201995591020,271663617600
解=/88141907439,181848600000,181848600000,202083916156,257172756418.56,202083916156,271858092561
解=/87695838144,182289600000,182289600000,202287069028,257796424599.567,202287069028,272304161856
解=/86747330871,183223800000,183223800000,202721632540,259117582909.535,202721632540,273252669129
解=/85875600791,184078200000,184078200000,203124106217,260325886977.227,203124106217,274124399209
解=/85868237519,184085400000,184085400000,203127518342,260336069314.876,203127518342,274131762481
解=/83761690271,186133800000,186133800000,204112254065,263232944376.041,204112254065,276238309729
解=/83581055804,186308400000,186308400000,204197484803,263479866064.032,204197484803,276418944196
解=/83298281039,186581400000,186581400000,204331158784,263865946366.559,204331158784,276701718961
解=/82025991936,187804800000,187804800000,204936346840,265596095238.767,204936346840,277974008064
解=/82000323599,187829400000,187829400000,204948619353,265630884892.401,204948619353,277999676401
解=/81987801239,187841400000,187841400000,204954607428,265647855455.15,204954607428,278012198761
解=/81986548959,187842600000,187842600000,204955206289,265649552511.424,204955206289,278013451041
解=/81610503759,188202600000,188202600000,205135304057,266158669393.879,205135304057,278389496241
解=/81417815516,188386800000,188386800000,205227793190,266419167532.068,205227793190,278582184484
解=/81029985975,188757000000,188757000000,205414370666,266942709392.858,205414370666,278970014025
解=/80324670204,189428400000,189428400000,205755124772,267892212378.636,205755124772,279675329796
解=/79549670279,190163400000,190163400000,206131678160,268931659346.98,206131678160,280450329721
解=/79118806076,190570800000,190570800000,206341986245,269507809952.291,206341986245,280881193924
解=/79060355900,190626000000,190626000000,206370569004,269585874540.934,206370569004,280939644100
解=/78025796444,191600400000,191600400000,206878559041,270963884236.11,206878559041,281974203556
解=/77583999375,192015000000,192015000000,207096685594,271550217179.07,207096685594,282416000625
解=/77570557884,192027600000,192027600000,207103333175,271568036269.956,207103333175,282429442116
解=/76927539599,192629400000,192629400000,207422110907,272419109991.792,207422110907,283072460401
解=/75700713884,193772400000,193772400000,208034470904,274035556093.584,208034470904,284299286116
解=/75075185759,194352600000,194352600000,208348786038,274856082802.473,208348786038,284924814241
解=/73519826031,195787800000,195787800000,209136384803,276885762107.191,209136384803,286480173969
解=/72435679100,196782000000,196782000000,209690445969,278291773230.902,209690445969,287564320900
解=/71997722231,197182200000,197182200000,209915440126,278857741498.564,209915440126,288002277769
解=/70570036796,198481200000,198481200000,210653546960,280694804916.087,210653546960,289429963204
解=/69823138959,199157400000,199157400000,211042509246,281651096126.963,211042509246,290176861041
解=/69716896079,199253400000,199253400000,211097993857,281786860628.951,211097993857,290283103921
解=/69667077104,199298400000,199298400000,211124024864,281850500239.258,211124024864,290332922896
解=/69190239839,199728600000,199728600000,211373609864,282458894913.791,211373609864,290809760161
解=/68821100775,200061000000,200061000000,211567359564,282928979501.924,211567359564,291178899225
解=/68602927356,200257200000,200257200000,211682091339,283206448202.861,211682091339,291397072644
解=/68491422959,200357400000,200357400000,211740791426,283348152401.811,211740791426,291508577041
解=/68102390879,200706600000,200706600000,211945924535,283841995777.792,211945924535,291897609121
解=/67825244375,200955000000,200955000000,212092375628,284193286426.685,212092375628,292174755625
解=/67525621616,201223200000,201223200000,212250997154,284572578504.114,212250997154,292474378384
解=/66466719191,202168200000,202168200000,212814017046,285909010320.556,212814017046,293533280809
解=/65922910991,202651800000,202651800000,213104627441,286592923999.32,213104627441,294077089009
解=/65486116799,203039400000,203039400000,213338766861,287141073176.096,213338766861,294513883201
解=/64646028956,203782800000,203782800000,213790875941,288192399538.364,213790875941,295353971044
解=/63548437500,204750000000,204750000000,214385089054,289560226895.891,214385089054,296451562500
解=/62797162199,205409400000,205409400000,214794099520,290492759318.92,214794099520,297202837801
解=/62592348096,205588800000,205588800000,214905925292,290746469232.01,214905925292,297407651904
解=/62539574375,205635000000,205635000000,214934761237,290811805898.591,214934761237,297460425625
解=/60600726236,207325200000,207325200000,216000431887,293202109661.714,216000431887,299399273764
解=/60042370199,207809400000,207809400000,216309576643,293886871868.615,216309576643,299957629801
解=/59218728704,208521600000,208521600000,216767422589,294894074767.738,216767422589,300781271296
解=/58639039839,209021400000,209021400000,217090954789,295600898706.212,217090954789,301360960161
解=/57319333436,210154800000,210154800000,217831462256,297203768357.805,217831462256,302680666564
解=/56503983600,210852000000,210852000000,218291699491,298189758053.492,218291699491,303496016400
解=/55757849600,211488000000,211488000000,218714681574,299089197879.161,218714681574,304242150400
解=/54377957376,212659200000,212659200000,219501475150,300745524803.412,219501475150,305622042624
解=/54204225671,212806200000,212806200000,219600949085,300953414197.081,219600949085,305795774329
解=/53899728764,213063600000,213063600000,219775518213,301317432768.036,219775518213,306100271236
解=/53677334439,213251400000,213251400000,219903196508,301583022075.05,219903196508,306322665561
解=/52703750204,214071600000,214071600000,220463909092,302742960038.908,220463909092,307296249796
解=/52125100784,214557600000,214557600000,220798527734,303430267830.222,220798527734,307874899216
解=/51481334975,215097000000,215097000000,221171985703,304193094625.766,221171985703,308518665025
解=/50297019551,216085800000,216085800000,221862261634,305591468996.24,221862261634,309702980449
解=/49191194375,217005000000,217005000000,222510547231,306891414102.774,222510547231,310808805625
解=/48890107719,217254600000,217254600000,222687682313,307244401807.942,222687682313,311109892281
解=/46641376511,219109800000,219109800000,224019022538,309868050808.856,224019022538,313358623489
解=/46285451100,219402000000,219402000000,224231087469,310281284011.782,224231087469,313714548900
解=/45932712896,219691200000,219691200000,224441612611,310690274574.02,224441612611,314067287104
解=/44633401916,220753200000,220753200000,225220149802,312192169377.26,225220149802,315366598084
解=/44347743900,220986000000,220986000000,225391957676,312521398294.581,225391957676,315652256100
解=/43883276400,221364000000,221364000000,225671802500,313055971021.158,225671802500,316116723600
解=/43517780775,221661000000,221661000000,225892443797,313475992449.183,225892443797,316482219225
解=/43080019271,222016200000,222016200000,226157204446,313978321106.538,226157204446,316919980729
解=/42108089756,222802800000,222802800000,226746949066,315090741494.7,226746949066,317891910244
解=/38314006256,225847200000,225847200000,229074050960,319396173263.989,229074050960,321685993744
解=/37594147311,226420200000,226420200000,229519992332,320206517635.229,229519992332,322405852689
解=/36200534319,227525400000,227525400000,230387252968,321769506464.363,230387252968,323799465681
解=/35803608176,227839200000,227839200000,230635208533,322213286680.236,230635208533,324196391824
解=/35613679676,227989200000,227989200000,230754002125,322425418714.592,230754002125,324386320324
解=/35494340679,228083400000,228083400000,230828693138,322558637632.168,230828693138,324505659321
解=/33631013276,229549200000,229549200000,231999741971,324631591871.894,231999741971,326368986724
解=/33447316316,229693200000,229693200000,232115680416,324835238624.876,232115680416,326552683684
解=/32829557616,230176800000,230176800000,232506213060,325519152303.639,232506213060,327170442384
解=/30712041116,231826800000,231826800000,233852292415,327852604681.555,233852292415,329287958884
解=/30646349631,231877800000,231877800000,233894234385,327924729573.236,233894234385,329353650369
解=/28464195824,233565600000,233565600000,235293646211,330311639223.809,235293646211,331535804176
解=/28323245151,233674200000,233674200000,235384447153,330465222816.683,235384447153,331676754849
解=/28299876831,233692200000,233692200000,235399505882,330490678660.806,235399505882,331700123169
解=/26503730204,235071600000,235071600000,236560996027,332441444848.743,236560996027,333496269796
解=/24800245884,236372400000,236372400000,237669862788,334281053850.678,237669862788,335199754116
解=/22651324416,238003200000,238003200000,239078660085,336587353328.196,239078660085,337348675584
解=/22360826556,238222800000,238222800000,239269950065,336897914626.493,239269950065,337639173444
解=/22290145871,238276200000,238276200000,239316522809,336973433630.724,239316522809,337709854129
解=/21825165056,238627200000,238627200000,239623200900,337469822591.117,239623200900,338174834944
解=/21064623111,239200200000,239200200000,240125912860,338280166962.357,240125912860,338935376889

主要是e都是小数（实际都是无理数）！

ysr

10000~50000之间解有2组解=/599964,2999640000,3999520000,2999640060,4999400000,3999520045,4999400036
解=/0,3000000000,4000000000,3000000000,5000000000,4000000000,5000000000


这回有一组没有0了！有一组合格的，是完美长方体吗？

200000~400000之间解有2组解=/943296008124,285751200000,381001600000,985627265879,476252000000,1017334545833,1056703991876
解=/921851238399,335461200000,447281600000,980991295804,559102000000,1024631902410,1078148761601

这些都是近似解，不是真的整数，换大数据程序了，可能解的数值过大，程序还在运行。

ysr

完美长方体就是此图中的线段abcdefg都是整数：

ysr

1000000~2000000之间解有9544组解=/24000000000000,6000000000000,8000000000000,24738633753706,10000000000000,25298221281347,26000000000000
解=/23999849994375,6000450000000,8000600000000,24738597372426,10000750000000,25298268717691,26000150005625
解=/23999573954631,6001278000000,8001704000000,24738530425979,10002130000000,25298356011951,26000426045369
解=/23999281871119,6002154000000,8002872000000,24738459591679,10003590000000,25298448382812,26000718128881
解=/23998977738879,6003066000000,8004088000000,24738385838845,10005110000000,25298544567286,26001022261121
解=/23998911704064,6003264000000,8004352000000,24738369825701,10005440000000,25298565451807,26001088295936
解=/23998599510000,6004200000000,8005600000000,24738294122299,10007000000000,25298664190059,26001400490000
解=/23998495434496,6004512000000,8006016000000,24738268886033,10007520000000,25298697107001,26001504565504
解=/23998469414775,6004590000000,8006120000000,24738262576826,10007650000000,25298705336564,26001530585225
解=/23998347317724,6004956000000,8006608000000,24738232971335,10008260000000,25298743953955,26001652682276
解=/23998329302775,6005010000000,8006680000000,24738228603207,10008350000000,25298749651847,26001670697225
解=/23997994995996,6006012000000,8008016000000,24738147545279,10010020000000,25298855390790,26002005004004
解=/23997964965711,6006102000000,8008136000000,24738140264173,10010170000000,25298864889358,26002035034289
解=/23997954955516,6006132000000,8008176000000,24738137837121,10010220000000,25298868055586,26002045044484
解=/23997826820604,6006516000000,8008688000000,24738106770122,10010860000000,25298908585017,26002173179396
解=/23997460389639,6007614000000,8010152000000,24738017930410,10012690000000,25299024491379,26002539610361
解=/23997382289136,6007848000000,8010464000000,24737998995918,10013080000000,25299049196091,26002617710864
解=/23996667227775,6009990000000,8013320000000,24737825649007,10016650000000,25299275394030,26003332772225
解=/23996551031271,6010338000000,8013784000000,24737797482206,10017230000000,25299312152607,26003448968729
解=/23996480909436,6010548000000,8014064000000,24737780484458,10017580000000,25299334335769,26003519090564
解=/23996356687600,6010920000000,8014560000000,24737750373163,10018200000000,25299373633988,26003643312400
解=/23996292570096,6011112000000,8014816000000,24737734831350,10018520000000,25299393918106,26003707429904
解=/23995723437504,6012816000000,8017088000000,24737596882863,10021360000000,25299573974455,26004276562496
解=/23995641260671,6013062000000,8017416000000,24737576965553,10021770000000,25299599973673,26004358739329
解=/23995124070775,6014610000000,8019480000000,24737451619437,10024350000000,25299763608427,26004875929225
解=/23994769177456,6015672000000,8020896000000,24737365613399,10026120000000,25299875899344,26005230822544
解=/23994751130359,6015726000000,8020968000000,24737361239933,10026210000000,25299881609701,26005248869641
解=/23994719046231,6015822000000,8021096000000,24737353464816,10026370000000,25299891761602,26005280953769