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勾股判断题

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发表于 2021-2-16 09:01 | 显示全部楼层
快速程序的结果出来了,是364组:
当x+y=163500169有364组解: /解/161972929/1527240/161980129其中(x + z) / 2=161976529其方根为:12727
/解/157623493/5876676/157733005其中(x + z) / 2=157678249其方根为:12557
/解/150390469/13109700/150960781其中(x + z) / 2=150675625其方根为:12275
/解/149309889/14190280/149982689其中(x + z) / 2=149646289其方根为:12233
/解/143472493/20027676/144863605其中(x + z) / 2=144168049其方根为:12007
/解/140300649/23199520/142205801其中(x + z) / 2=141253225其方根为:11885
/解/130066893/33433276/134295125其中(x + z) / 2=132181009其方根为:11497
/解/117071293/46428876/125941765其中(x + z) / 2=121506529其方根为:11023
/解/113764249/49735920/124161049其中(x + z) / 2=118962649其方根为:10907
/解/111035493/52464676/122806445其中(x + z) / 2=116920969其方根为:10813
/解/102080889/61419280/119133689其中(x + z) / 2=110607289其方根为:10517
/解/96547329/66952840/117490721其中(x + z) / 2=107019025其方根为:10345
/解/91172469/72327700/116377469其中(x + z) / 2=103774969其方根为:10187
/解/90326569/73173600/116246569其中(x + z) / 2=103286569其方根为:10163
/解/85733493/77766676/115749245其中(x + z) / 2=100741369其方根为:10037
/解/84902449/78597720/115698001其中(x + z) / 2=100300225其方根为:10015
/解/82585929/80914240/115618121其中(x + z) / 2=99102025其方根为:9955
/解/76331893/87168276/115865725其中(x + z) / 2=96098809其方根为:9803
/解/73768209/89731960/116161841其中(x + z) / 2=94965025其方根为:9745
/解/70989049/92511120/116609401其中(x + z) / 2=93799225其方根为:9685
/解/69152509/94347660/116976709其中(x + z) / 2=93064609其方根为:9647
/解/57284589/106215580/120678389其中(x + z) / 2=88981489其方根为:9433
/解/53981793/109518376/122099585其中(x + z) / 2=88040689其方根为:9383
/解/48192609/115307560/124973441其中(x + z) / 2=86583025其方根为:9305
/解/42041449/121458720/128529001其中(x + z) / 2=85285225其方根为:9235
/解/28742169/134758000/137789081其中(x + z) / 2=83265625其方根为:9125
/解/24952509/138547660/140776709其中(x + z) / 2=82864609其方根为:9103
/解/19284793/144215376/145499065其中(x + z) / 2=82391929其方根为:9077
/解/18223293/145276876/146415365其中(x + z) / 2=82319329其方根为:9073
/解/11228709/152271460/152684909其中(x + z) / 2=81956809其方根为:9053
/解/7819393/155680776/155877025其中(x + z) / 2=81848209其方根为:9047
/解/4053993/159446176/159497705其中(x + z) / 2=81775849其方根为:9043
/解/162219645/1280524/162224699其中(x + z) / 2=162222172其方根为:12736.6468114649
/解/146742925/16757244/147696619其中(x + z) / 2=147219772其方根为:12133.4155125422
/解/142770985/20729184/144267991其中(x + z) / 2=143519488其方根为:11979.9619365005
/解/136137001/27363168/138859735其中(x + z) / 2=137498368其方根为:11725.9698106383
/解/108303825/55196344/121558031其中(x + z) / 2=114930928其方根为:10720.5843124337
/解/96368545/67131624/117445951其中(x + z) / 2=106907248其方根为:10339.5961236404
/解/87731245/75768924/115921099其中(x + z) / 2=101826172其方根为:10090.8955004003
/解/85171905/78328264/115713311其中(x + z) / 2=100442608其方根为:10022.1059663127
/解/79761465/83738704/115646279其中(x + z) / 2=97703872其方根为:9884.52689813731
/解/74331705/89168464/116087111其中(x + z) / 2=95209408其方根为:9757.53083520621
/解/71166501/92333668/116576915其中(x + z) / 2=93871708其方根为:9688.74130111853
/解/59358901/104141268/119870275其中(x + z) / 2=89614588其方根为:9466.4981909891
/解/25634301/137865868/140228795其中(x + z) / 2=82931548其方根为:9106.67601268432
/解/22507345/140992824/142777999其中(x + z) / 2=82642672其方根为:9090.80150481793
/解/11583901/151916268/152357275其中(x + z) / 2=81970588其方根为:9053.76098646303
/解/4296565/159203604/159261571其中(x + z) / 2=81779068其方根为:9043.17798121877
/解/155879205/7620964/156065389其中(x + z) / 2=155972297其方根为:12488.8869399959
/解/137115625/26384544/139631081其中(x + z) / 2=138373353其方根为:11763.2203498872
/解/131669301/31830868/135462205其中(x + z) / 2=133565753其方根为:11557.0650686063
/解/121622301/41877868/128630245其中(x + z) / 2=125126273其方根为:11185.9855623007
/解/112293585/51206584/123417841其中(x + z) / 2=117855713其方根为:10856.1371122513
/解/106679301/56820868/120868045其中(x + z) / 2=113773673其方根为:10666.4742534729
/解/101074605/62425564/118798261其中(x + z) / 2=109936433其方根为:10485.0576059457
/解/92362785/71137384/116582209其中(x + z) / 2=104472497其方根为:10221.1788459062
/解/75147225/88352944/115988569其中(x + z) / 2=95567897其方根为:9775.88343833947
/解/66501501/96998668/117606085其中(x + z) / 2=92053793其方根为:9594.4667908123
/解/52620865/110879304/122732129其中(x + z) / 2=87676497其方根为:9363.57287577771
/解/46911925/116588244/125672381其中(x + z) / 2=86292153其方根为:9289.35697451659
/解/37392265/126107904/131534729其中(x + z) / 2=84463497其方根为:9190.40243950177
/解/36445365/127054804/132178621其中(x + z) / 2=84311993其方根为:9182.15622825053
/解/31136401/132363768/135976625其中(x + z) / 2=83556513其方根为:9140.92517199435
/解/2148001/161352168/161366465其中(x + z) / 2=81757233其方根为:9041.97063697953
/解/150203685/13296484/150791059其中(x + z) / 2=150497372其方根为:12267.7370366339
/解/135754165/27746004/138560579其中(x + z) / 2=137157372其方根为:11711.4205799297
/解/125766001/37734168/131304815其中(x + z) / 2=128535408其方根为:11337.3457211113
/解/122885205/40614964/129423139其中(x + z) / 2=126154172其方根为:11231.8374275984
/解/117821065/45679104/126366071其中(x + z) / 2=122093568其方根为:11049.5958297125
/解/105498585/58001584/120391591其中(x + z) / 2=112945088其方根为:10627.562655661
/解/102239301/61260868/119187955其中(x + z) / 2=110713628其方根为:10522.0543621481
/解/96692805/66807364/117527539其中(x + z) / 2=107110172其方根为:10349.4044273088
/解/65348865/98151304/117915871其中(x + z) / 2=91632368其方根为:9572.47972053219
/解/62734501/100765668/118698515其中(x + z) / 2=90716508其方根为:9524.52140529906
/解/53819425/109680744/122173631其中(x + z) / 2=87996528其方根为:9380.64645959968
/解/42212245/121287924/128423651其中(x + z) / 2=85317948其方根为:9236.7715139003
/解/41276145/122224024/129005551其中(x + z) / 2=85140848其方根为:9227.17985085367
/解/36100501/127399668/132415715其中(x + z) / 2=84258108其方根为:9179.22153562055
/解/32462545/131037624/134998799其中(x + z) / 2=83730672其方根为:9150.44654648067
/解/18417825/145082344/146246719其中(x + z) / 2=82332272其方根为:9073.71324210767
/解/149723769/13776400/150356231其中(x + z) / 2=150040000其方根为:12249.081598226
/解/142819449/20680720/144308999其中(x + z) / 2=143564224其方根为:11981.8289088102
/解/123298129/40202040/129686671其中(x + z) / 2=126492400其方根为:11246.8840129166
/解/120224169/43276000/127775831其中(x + z) / 2=124000000其方根为:11135.52872566
/解/117418669/46081500/126137419其中(x + z) / 2=121778044其方根为:11035.3089671291
/解/110697249/52802920/122645951其中(x + z) / 2=116671600其方根为:10801.4628638902
/解/102619393/60880776/119319775其中(x + z) / 2=110969584其方根为:10534.2101744744
/解/90851793/72648376/116326415其中(x + z) / 2=103589104其方根为:10177.8732552533
/解/76651189/86848980/115836739其中(x + z) / 2=96243964其方根为:9810.4008073065
/解/64972869/98527300/118021619其中(x + z) / 2=91497244其方根为:9565.41917534198
/解/48536793/114963376/124789415其中(x + z) / 2=86663104其方根为:9309.3020146518
/解/47638909/115861260/125272891其中(x + z) / 2=86455900其方根为:9298.16648592614
/解/41686909/121813260/128748859其中(x + z) / 2=85217884其方根为:9231.35331357218
/解/35677993/127822176/132708055其中(x + z) / 2=84193024其方根为:9175.67566994388
/解/18883309/144616860/145844491其中(x + z) / 2=82363900其方根为:9075.45591141294
/解/15628929/147871240/148694879其中(x + z) / 2=82161904其方根为:9064.32038268728
/解/161870829/1629340/161879029其中(x + z) / 2=161874929其方根为:12723.0078597791
/解/153345289/10154880/153681161其中(x + z) / 2=153513225其方根为:12390.0453994326
/解/146425309/17074860/147417509其中(x + z) / 2=146921409其方根为:12121.1141814604
/解/126530469/36969700/131820781其中(x + z) / 2=129175625其方根为:11365.5455214433
/解/98927793/64572376/118136785其中(x + z) / 2=108532289其方根为:10417.8831343032
/解/94273309/69226860/116960741其中(x + z) / 2=105617025其方根为:10277.0144010797
/解/87980793/75519376/115947385其中(x + z) / 2=101964089其方根为:10097.7269224316
/解/82658829/80841340/115619221其中(x + z) / 2=99139025其方根为:9956.85818920808
/解/74081793/89418376/116119585其中(x + z) / 2=95100689其方根为:9751.95821361023
/解/66033493/97466676/117729245其中(x + z) / 2=91881369其方根为:9585.47698343697
/解/57208489/106291680/120709289其中(x + z) / 2=88958889其方根为:9431.80200173859
/解/44846169/118654000/126846169其中(x + z) / 2=85846169其方根为:9265.32077156533
/解/38596129/124904040/130731329其中(x + z) / 2=84663729其方根为:9201.289529191
/解/28655269/134844900/137855981其中(x + z) / 2=83255625其方根为:9124.45203834181
/解/14285589/149214580/149896861其中(x + z) / 2=82091225其方根为:9060.42079596748
/解/8239729/155260440/155478929其中(x + z) / 2=81859329其方根为:9047.61454749261
/解/153473001/10027168/153800215其中(x + z) / 2=153636608其方根为:12395.0235175251
/解/139297801/24202368/141384695其中(x + z) / 2=140341248其方根为:11846.571149493
/解/132803905/30696264/136305311其中(x + z) / 2=134554608其方根为:11599.7675838786
/解/120551005/42949164/127973339其中(x + z) / 2=124262172其方根为:11147.2943802521
/解/117096505/46403664/125955911其中(x + z) / 2=121526208其方根为:11023.8925974449
/解/110383965/53116204/122498779其中(x + z) / 2=116441372其方根为:10790.8003410312
/解/102924501/60575668/119427235其中(x + z) / 2=111175868其方根为:10543.9967754168
/解/82562785/80937384/115617791其中(x + z) / 2=99090288其方根为:9954.41047978232
/解/76947225/86552944/115811431其中(x + z) / 2=96379328其方根为:9817.2973877743
/解/57308745/106191424/120668599其中(x + z) / 2=88988672其方根为:9433.38073015184
/解/56429845/107070324/121030499其中(x + z) / 2=88730172其方根为:9419.66942095104
/解/50707501/112792668/123666635其中(x + z) / 2=87187068其方根为:9337.40156574622
/解/38487501/125012668/130803115其中(x + z) / 2=84645308其方根为:9200.2884737382
/解/35338501/128161668/132944435其中(x + z) / 2=84141468其方根为:9172.8658553366
/解/19255665/144244504/145524079其中(x + z) / 2=82389872其方根为:9076.88669093098
/解/15248445/148251724/149033851其中(x + z) / 2=82141148其方根为:9063.17538173018
/解/134723589/28776580/137762611其中(x + z) / 2=136243100其方根为:11672.3219626602
/解/124788993/38711176/130655455其中(x + z) / 2=127722224其方根为:11301.4257507626
/解/118765689/44734480/126911239其中(x + z) / 2=122838464其方根为:11083.2515084699
/解/94975209/68524960/117115159其中(x + z) / 2=106045184其方根为:10297.8242362161
/解/64468369/99031800/118167119其中(x + z) / 2=91317744其方根为:9556.03181242089
/解/49069293/114430876/124507915其中(x + z) / 2=86788604其方根为:9316.0401458989
/解/34151929/129348240/133780871其中(x + z) / 2=83966400其方根为:9163.318176294
/解/23960293/139539876/141582035其中(x + z) / 2=82771164其方根为:9097.86590360619
/解/129696609/33803560/134029441其中(x + z) / 2=131863025其方根为:11483.1626741068
/解/123514209/39985960/129825409其中(x + z) / 2=126669809其方根为:11254.7682783787
/解/120011493/43488676/127648045其中(x + z) / 2=123829769其方根为:11127.8825029742
/解/107582293/55917876/121246685其中(x + z) / 2=114414489其方根为:10696.4708665989
/解/60070549/103429620/119608349其中(x + z) / 2=89839449其方根为:9478.36742271579
/解/47847429/115652740/125159629其中(x + z) / 2=86503529其方根为:9300.7273371495
/解/38370969/125129200/130880281其中(x + z) / 2=84625625其方根为:9199.2187168259
/解/35456869/128043300/132861869其中(x + z) / 2=84159369其方根为:9173.841561745
/解/136520125/26980044/139160581其中(x + z) / 2=137840353其方根为:11740.543130537
/解/123100845/40399324/129560501其中(x + z) / 2=126330673其方根为:11239.6918552067
/解/107969001/55531168/121412585其中(x + z) / 2=114690793其方根为:10709.3787401511
/解/105298165/58202004/120312829其中(x + z) / 2=112805497其方根为:10620.9932209751
/解/59689105/103811064/119747761其中(x + z) / 2=89718433其方根为:9471.98147168796
/解/54022801/109477368/122080945其中(x + z) / 2=88051873其方根为:9383.59595251202
/解/35879865/127620304/132568121其中(x + z) / 2=84223993其方根为:9177.36307443483
/解/22113385/141386784/143105641其中(x + z) / 2=82609513其方根为:9088.9775552589
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发表于 2021-2-16 09:02 | 显示全部楼层
/解/157963365/5536804/158060371其中(x + z) / 2=158011868其方根为:12570.2771648043
/解/146649825/16850344/147614719其中(x + z) / 2=147132272其方根为:12129.8092318057
/解/132483505/31016664/136065839其中(x + z) / 2=134274672其方根为:11587.6948527306
/解/99501465/63998704/118306279其中(x + z) / 2=108903872其方根为:10435.701797196
/解/82834801/80665368/115622255其中(x + z) / 2=99228528其方根为:9961.35171550528
/解/71240001/92260168/116563615其中(x + z) / 2=93901808其方根为:9690.29452596772
/解/62530125/100970044/118764331其中(x + z) / 2=90647228其方根为:9520.88378250675
/解/7483525/156016644/156196019其中(x + z) / 2=81839772其方根为:9046.53370081602
/解/146772493/16727676/147722645其中(x + z) / 2=147247569其方根为:12134.5609314882
/解/122769969/40730200/129349969其中(x + z) / 2=126059969其方根为:11227.6430741274
/解/108279493/55220676/121547405其中(x + z) / 2=114913449其方根为:10719.7690740053
/解/104990809/58509360/120193241其中(x + z) / 2=112592025其方根为:10610.938931122
/解/62628769/100871400/118732481其中(x + z) / 2=90680625其方根为:9522.63750228895
/解/50995329/112504840/123522721其中(x + z) / 2=87259025其方根为:9341.25393081678
/解/45144393/118355776/126673225其中(x + z) / 2=85908809其方根为:9268.70050222792
/解/21747229/141752940/143411429其中(x + z) / 2=82579329其方根为:9087.31693075574
/解/156086809/7413360/156262759其中(x + z) / 2=156174784其方根为:12496.9909978362
/解/144896389/18603780/146085811其中(x + z) / 2=145491100其方根为:12061.969159304
/解/100916709/62583460/118747091其中(x + z) / 2=109831900其方根为:10480.0715646412
/解/86035249/77464920/115770799其中(x + z) / 2=100903024其方根为:10045.0497261089
/解/81454293/82045876/115612835其中(x + z) / 2=98533564其方根为:9926.40740650916
/解/58463493/105036676/120210995其中(x + z) / 2=89337244其方根为:9451.83812811032
/解/23569089/139931080/141902111其中(x + z) / 2=82735600其方根为:9095.91116931119
/解/12716493/150783676/151318955其中(x + z) / 2=82017724其方根为:9056.36372944462
/解/162914145/586024/162915199其中(x + z) / 2=162914672其方根为:12763.8031949729
/解/128332405/35167764/133063811其中(x + z) / 2=130698108其方根为:11432.327322116
/解/100538425/62961744/118626119其中(x + z) / 2=109582272其方根为:10468.1551383231
/解/86404285/77095884/115799291其中(x + z) / 2=101101788其方根为:10054.9384881261
/解/81085801/82414368/115615895其中(x + z) / 2=98350848其方根为:9917.19960472713
/解/58846401/104653768/120063775其中(x + z) / 2=89455088其方根为:9458.06999339717
/解/30521205/132978964/136436611其中(x + z) / 2=83478908其方根为:9136.6792654662
/解/6110565/157389604/157508179其中(x + z) / 2=81809372其方根为:9044.85334320021
/解/151782205/11717964/152233861其中(x + z) / 2=152008033其方根为:12329.1537828028
/解/140867185/22632984/142673809其中(x + z) / 2=141770497其方根为:11906.7416617646
/解/109033801/54466368/121880905其中(x + z) / 2=115457353其方根为:10745.1083289095
/解/104246805/59253364/119909789其中(x + z) / 2=112078297其方根为:10586.7037835202
/解/78226401/85273768/115719425其中(x + z) / 2=96972913其方根为:9847.48257170329
/解/49337145/114163024/124367801其中(x + z) / 2=86852473其方根为:9319.46742040552
/解/39927645/123572524/129862949其中(x + z) / 2=84895297其方根为:9213.86439014597
/解/33863745/129636424/133986401其中(x + z) / 2=83925073其方根为:9161.0628750162
/解/158127001/5373168/158218265其中(x + z) / 2=158172633其方根为:12576.6701872952
/解/143011401/20488768/144471625其中(x + z) / 2=143741513其方根为:11989.2248706912
/解/96173005/67327164/117397589其中(x + z) / 2=106785297其方根为:10333.6971602617
/解/90697165/72803004/116302421其中(x + z) / 2=103499793其方根为:10173.4848011878
/解/71360605/92139564/116541989其中(x + z) / 2=93951297其方根为:9692.84772396637
/解/68779545/94720624/117058201其中(x + z) / 2=92918873其方根为:9639.44360427509
/解/25400625/138099544/140416081其中(x + z) / 2=82908353其方根为:9105.40240736235
/解/10741345/152758824/153136001其中(x + z) / 2=81938673其方根为:9051.99828767107
/解/151655793/11844376/152117615其中(x + z) / 2=151886704其方根为:12324.2323898894
/解/127992609/35507560/132826559其中(x + z) / 2=130409584其方根为:11419.7015722829
/解/100235349/63264820/118530851其中(x + z) / 2=109383100其方根为:10458.6375785759
/解/86700289/76799880/115823839其中(x + z) / 2=101262064其方根为:10062.905345873
/解/72797689/90702480/116303239其中(x + z) / 2=94550464其方根为:9723.70628927057
/解/67332529/96167640/117396271其中(x + z) / 2=92364400其方根为:9610.63993706975
/解/40035493/123464676/129793555其中(x + z) / 2=84914524其方根为:9214.90770436687
/解/6512649/156987520/157122551其中(x + z) / 2=81817600其方根为:9045.30817606564
/解/139476301/24023868/141530155其中(x + z) / 2=140503228其方根为:11853.4057553093
/解/114486801/49013368/124537295其中(x + z) / 2=119512048其方根为:10932.1566033423
/解/105422685/58077484/120361691其中(x + z) / 2=112892188其方根为:10625.0735526866
/解/93578605/69921564/116816011其中(x + z) / 2=105197308其方根为:10256.5738918998
/解/50551401/112948768/123745175其中(x + z) / 2=87148288其方根为:9335.32473993272
/解/45598765/117901404/126411979其中(x + z) / 2=86005372其方根为:9273.90812980159
/解/32547645/130952524/134936699其中(x + z) / 2=83742172其方根为:9151.07490953932
/解/22261401/141238768/142982375其中(x + z) / 2=82621888其方根为:9089.65829940818
/解/158531893/4968276/158609725其中(x + z) / 2=158570809其方根为:12592.4901826446
/解/132972729/30527440/136431929其中(x + z) / 2=134702329其方根为:11606.1332492782
/解/99076893/64423276/118180325其中(x + z) / 2=108628609其方根为:10422.5049292385
/解/87834493/75665676/115931845其中(x + z) / 2=101883169其方根为:10093.719284783
/解/71658409/91841760/116489641其中(x + z) / 2=94074025其方根为:9699.17651143642
/解/68480269/95019900/117125269其中(x + z) / 2=92802769其方根为:9633.41938254533
/解/25759149/137741020/140128949其中(x + z) / 2=82944049其方根为:9107.36235141657
/解/593469/162906700/162907781其中(x + z) / 2=81750625其方根为:9041.60522252548
/解/153769393/9730776/154076975其中(x + z) / 2=153923184其方根为:12406.5782551032
/解/139025793/24474376/141163615其中(x + z) / 2=140094704其方根为:11836.160864064
/解/119879449/43620720/127568999其中(x + z) / 2=123724224其方根为:11123.139125265
/解/93951049/69549120/116892599其中(x + z) / 2=105421824其方根为:10267.5130387061
/解/68098909/95401260/117212891其中(x + z) / 2=92655900其方根为:9625.79347378698
/解/50945493/112554676/123547555其中(x + z) / 2=87246524其方根为:9340.58477826736
/解/45195489/118304680/126643711其中(x + z) / 2=85919600其方根为:9269.28260438746
/解/38235493/125264676/130970195其中(x + z) / 2=84602844其方根为:9197.98043050756
/解/161559445/1940724/161571101其中(x + z) / 2=161565273其方根为:12710.8328995389
/解/139937565/23562604/141907429其中(x + z) / 2=140922497其方根为:11871.0781734432
/解/110721801/52778368/122657545其中(x + z) / 2=116689673其方根为:10802.2994311397
/解/82881445/80618724/115623149其中(x + z) / 2=99252297其方根为:9962.54470504399
/解/76628001/86872168/115838785其中(x + z) / 2=96233393其方根为:9809.86202757205
/解/56975985/106524184/120804241其中(x + z) / 2=88890113其方根为:9428.1553338922
/解/28389645/135110524/138060949其中(x + z) / 2=83225297其方根为:9122.78997894833
/解/7420501/156079668/156255965其中(x + z) / 2=81838233其方根为:9046.44864021236
/解/130178485/33321684/134375491其中(x + z) / 2=132276988其方根为:11501.1733314475
/解/123048585/40451584/129527159其中(x + z) / 2=126287872其方根为:11237.7876826358
/解/108017985/55482184/121433759其中(x + z) / 2=114725872其方根为:10711.0163850122
/解/91075801/72424368/116361895其中(x + z) / 2=103718848其方根为:10184.2450873887
/解/65200045/98300124/117957451其中(x + z) / 2=91578748其方根为:9569.67857349451
/解/48296401/115203768/124917775其中(x + z) / 2=86607088其方根为:9306.29292468274
/解/29627625/133872544/137111831其中(x + z) / 2=83369728其方根为:9130.70249214155
/解/3921445/159578724/159626899其中(x + z) / 2=81774172其方根为:9042.90727587096
/解/148194865/15305304/148983121其中(x + z) / 2=148588993其方根为:12189.7084870804
/解/84039585/79460584/115657409其中(x + z) / 2=99848497其方根为:9992.42197867964
/解/75467301/88032868/115953005其中(x + z) / 2=95710153其方根为:9783.15659692719
/解/10085845/153414324/153745501其中(x + z) / 2=81915673其方根为:9050.7277607936
/解/148670389/14829780/149408189其中(x + z) / 2=149039289其方根为:12208.1648498044
/解/97894993/65605176/117845105其中(x + z) / 2=107870049其方根为:10386.0506931172
/解/69652009/93848160/116871209其中(x + z) / 2=93261609其方根为:9657.2050304423
/解/9595089/153905080/154203889其中(x + z) / 2=81899489其方根为:9049.83364487989
/解/121345609/42154560/128459191其中(x + z) / 2=124902400其方根为:11175.9742304642
/解/61314393/102185776/119169575其中(x + z) / 2=90241984其方根为:9499.57809589457
/解/52356549/111143620/122858099其中(x + z) / 2=87607324其方根为:9359.87841801377
/解/20155149/143345020/144755051其中(x + z) / 2=82455100其方根为:9080.47906225217
/解/161703409/1796760/161713391其中(x + z) / 2=161708400其方根为:12716.4617720496
/解/85540749/77959420/115736299其中(x + z) / 2=100638524其方根为:10031.8753979503
/解/73961629/89538540/116135579其中(x + z) / 2=95048604其方根为:9749.2873585714
/解/3788169/159712000/159756919其中(x + z) / 2=81772544其方根为:9042.81726012419
/解/159719301/3780868/159764045其中(x + z) / 2=159741673其方根为:12638.8952444428
/解/98196301/65303868/117928405其中(x + z) / 2=108062353其方根为:10395.3043726483
/解/61215385/102284784/119203609其中(x + z) / 2=90209497其方根为:9497.86802393042
/解/9200485/154299684/154573741其中(x + z) / 2=81887113其方根为:9049.14984957151
/解/133293993/30206176/136673705其中(x + z) / 2=134983849其方根为:11618.2549894552
/解/120091993/43408176/127696345其中(x + z) / 2=123894169其方根为:11130.7757591284
/解/110824189/52675980/122705989其中(x + z) / 2=116765089其方根为:10805.7896055772
/解/51151149/112349020/123445301其中(x + z) / 2=87298225其方根为:9343.35191459682
/解/161290605/2209564/161305739其中(x + z) / 2=161298172其方根为:12700.3217282083
/解/93853501/69646668/116872315其中(x + z) / 2=105362908其方根为:10264.6435885519
/解/73664745/89835424/116176151其中(x + z) / 2=94920448其方根为:9742.71255862555
/解/7680505/155819664/156008839其中(x + z) / 2=81844672其方根为:9046.80451872372
/解/132858901/30641268/136346525其中(x + z) / 2=134602713其方根为:11601.8409315074
/解/62857305/100642864/118659289其中(x + z) / 2=90758297其方根为:9526.71491123777
/解/50757385/112742784/123641609其中(x + z) / 2=87199497其方根为:9338.06709121326
/解/32322801/131177368/135100945其中(x + z) / 2=83711873其方根为:9149.41927118875
/解/146365849/17134320/147365351其中(x + z) / 2=146865600其方根为:12118.811822947
/解/88027569/75472600/115952431其中(x + z) / 2=101990000其方根为:10099.0098524558
/解/71464393/92035776/116523575其中(x + z) / 2=93993984其方根为:9695.0494583576
/解/22142029/141358140/143081771其中(x + z) / 2=82611900其方根为:9089.10886721025
/解/137561229/25938940/139985429其中(x + z) / 2=138773329其方根为:11780.2092086686
/解/107064793/56435376/121028185其中(x + z) / 2=114046489其方根为:10679.2550770173
/解/52229389/111270780/122919061其中(x + z) / 2=87574225其方根为:9358.11011903579
/解/30702493/132797676/136300645其中(x + z) / 2=83501569其方根为:9137.91929270553
/解/136252389/27247780/138950189其中(x + z) / 2=137601289其方根为:11730.3575819324
/解/117367789/46132380/126108661其中(x + z) / 2=121738225其方根为:11033.5046562731
/解/96270993/67229176/117421745其中(x + z) / 2=106846369其方根为:10336.6517306137
/解/35624449/127875720/132745249其中(x + z) / 2=84184849其方根为:9175.23018784815
/解/160293969/3206200/160326031其中(x + z) / 2=160310000其方根为:12661.3585369027
/解/97773069/65727100/117811819其中(x + z) / 2=107792444其方根为:10382.3140002603
/解/89116329/74383840/116080471其中(x + z) / 2=102598400其方根为:10129.0868295222
/解/27300793/136199376/138908615其中(x + z) / 2=83104704其方根为:9116.17814656998
/解/137919385/25580784/140271641其中(x + z) / 2=139095513其方根为:11793.8760804072
/解/115866985/47633184/125276009其中(x + z) / 2=120571497其方根为:10980.5053162411
/解/51915025/111585144/123070769其中(x + z) / 2=87492897其方根为:9353.76378790912
/解/20674125/142826044/144314581其中(x + z) / 2=82494353其方根为:9082.64019985378
/解/159783765/3716404/159826979其中(x + z) / 2=159805372其方根为:12641.414952449
/解/84159265/79340904/115662271其中(x + z) / 2=99910768其方根为:9995.53740426196
/解/55638025/107862144/121366519其中(x + z) / 2=88502272其方根为:9407.56461577597
/解/26857501/136642668/139257115其中(x + z) / 2=83057308其方根为:9113.57822153297
/解/121293793/42206376/128427265其中(x + z) / 2=124860529其方根为:11174.1008139358
/解/92660829/70839340/116637221其中(x + z) / 2=104649025其方根为:10229.8106043074
/解/66801993/96698176/117528905其中(x + z) / 2=92165449其方根为:9600.28379788848
/解/46590489/116909680/125851289其中(x + z) / 2=86220889其方根为:9285.52039467902
/解/146895825/16604344/147831281其中(x + z) / 2=147363553其方根为:12139.3390676758
/解/99304501/64195668/118247485其中(x + z) / 2=108775993其方根为:10429.573001806
/解/87611301/75888868/115908845其中(x + z) / 2=101760073其方根为:10087.619788632
/解/14762665/148737504/149468329其中(x + z) / 2=82115497其方根为:9061.76014911011
/解/141879229/21620940/143517179其中(x + z) / 2=142698204其方根为:11945.6353535507
/解/112396129/51104040/123468671其中(x + z) / 2=117932400其方根为:10859.6685032279
/解/75050869/88449300/115999619其中(x + z) / 2=95525244其方根为:9773.70165290511
/解/9532869/153967300/154262131其中(x + z) / 2=81897500其方根为:9049.72375268991
/解/126101893/37398276/131530675其中(x + z) / 2=128816284其方根为:11349.7261640975
/解/105191029/58309140/120270979其中(x + z) / 2=112731004其方根为:10617.4857664138
/解/62430993/101069176/118796495其中(x + z) / 2=90613744其方根为:9519.12516988825
/解/32807269/130692900/134747731其中(x + z) / 2=83777500其方根为:9153.00497104639
/解/143289793/20210376/144708065其中(x + z) / 2=143998929其方根为:11999.955374917
/解/80176689/83323480/115633489其中(x + z) / 2=97905089其方根为:9894.70004598421
/解/59789029/103711140/119711021其中(x + z) / 2=89750025其方根为:9473.64898019765
/解/11035929/152464240/152863129其中(x + z) / 2=81949529其方根为:9052.59791441109
/解/129808501/33691668/134109565其中(x + z) / 2=131959033其方根为:11487.3422948914
/解/101851585/61648584/119055841其中(x + z) / 2=110453713其方根为:10509.6961421347
/解/85125225/78374944/115710569其中(x + z) / 2=100417897其方根为:10020.8730657563
/解/4360801/159139368/159199105其中(x + z) / 2=81779953其方根为:9043.22691299959
/解/118361565/45138604/126676571其中(x + z) / 2=122519068其方根为:11068.8331815056
/解/49465801/114034368/124300855其中(x + z) / 2=86883328其方根为:9321.12267916263
/解/72379965/91120204/116369029其中(x + z) / 2=94374497其方根为:9714.65372517209
/解/5947501/157552668/157664885其中(x + z) / 2=81806193其方根为:9044.67760619471
/解/109471789/54028380/122078411其中(x + z) / 2=115775100其方根为:10759.8838283692
/解/49783293/113716876/124136635其中(x + z) / 2=86959964其方根为:9325.23265125327
/解/144745293/18754876/145955285其中(x + z) / 2=145350289其方根为:12056.1307640553
/解/72750769/90749400/116310481其中(x + z) / 2=94530625其方根为:9722.68610004458
/解/134371825/29128344/137492719其中(x + z) / 2=135932272其方根为:11658.9996140321
/解/33809685/129690484/134025059其中(x + z) / 2=83917372其方根为:9160.64255388234
/解/82466293/81033876/115616515其中(x + z) / 2=99041404其方根为:9951.95478285548
/解/7980609/155519560/155724191其中(x + z) / 2=81852400其方根为:9047.23162077771
/解/86451001/77049168/115803065其中(x + z) / 2=101127033其方根为:10056.1937630497
/解/24077865/139422304/141486121其中(x + z) / 2=82781993其方根为:9098.46102371165
/解/120338001/43162168/127844465其中(x + z) / 2=124091233其方根为:11139.6244550703
/解/38705205/124794964/130659389其中(x + z) / 2=84682297其方根为:9202.29846288415
/解/149849301/13650868/150469795其中(x + z) / 2=150159548其方根为:12253.9605026293
/解/85317925/78182244/115722131其中(x + z) / 2=100520028其方根为:10025.9676839695
/解/96594729/66905440/117502679其中(x + z) / 2=107048704其方根为:10346.4343616533
/解/11290293/152209876/152628035其中(x + z) / 2=81959164其方根为:9053.13006644663
/解/103864849/59635320/119767601其中(x + z) / 2=111816225其方根为:10574.3191270171
/解/34290309/129209860/133682509其中(x + z) / 2=83986409其方根为:9164.4099100815
/解/145270185/18229984/146409559其中(x + z) / 2=145839872其方根为:12076.4180119769
/解/13102801/150397368/150967055其中(x + z) / 2=82034928其方根为:9057.31350898267
/解/124320405/39179764/130348061其中(x + z) / 2=127334233其方根为:11284.2471171098
/解/64043845/99456324/118292749其中(x + z) / 2=91168297其方根为:9548.20909909288
/解/118816893/44683276/126941125其中(x + z) / 2=122879009其方根为:11085.0804688103
/解/17263993/146236176/147251705其中(x + z) / 2=82257849其方根为:9069.61129266299
/解/136021149/27479020/138769051其中(x + z) / 2=137395100其方根为:11721.5655950901
/解/53584089/109916080/122281639其中(x + z) / 2=87932864其方根为:9377.25247607208
/解/121755445/41744724/128712899其中(x + z) / 2=125234172其方根为:11190.8074775684
/解/83743989/79756180/115646461其中(x + z) / 2=99695225其方根为:9984.74962129747
/解/36919393/126580776/131854975其中(x + z) / 2=84387184其方根为:9186.2497244523
/解/106630545/56869624/120847951其中(x + z) / 2=113739248其方根为:10664.8604304041
/解/48088285/115411884/125029541其中(x + z) / 2=86558913其方根为:9303.70426228177
/解/70071501/93428668/116785835其中(x + z) / 2=93428668其方根为:9665.85060923248
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发表于 2021-2-16 09:08 | 显示全部楼层
快速程序的代码:

Private Sub Command1_Click()
Dim a, b, x, y, z, m
m = Text2
b1 = m / 2
b2 = b1 / 3
s1 = 0
Do While t < Val(b2) + 2
t = t + 1
b = 0
Do While t * b ^ 2 < Val(b1) + 2
a = b
b = b + 1
Do While t * a ^ 2 < Val(m)
a = a + 1
x = t * (a ^ 2 - b ^ 2)
y = 2 * a * b * t
z = Sqr(x ^ 2 + y ^ 2)
If InStr(z, ".") = 0 And x + y = Val(m) Then
m1 = (x + z) / 2
m2 = Sqr(m1)
s = s & "/解/" & x & "/" & y & "/" & z & "其中(x + z) / 2=" & m1 & "其方根为:" & m2 & vbCrLf
s1 = s1 + 1
Else
s1 = s1
End If
Loop
Loop
Loop


Text1 = Text1 & "当x+y=" & m & "有" & s1 + s2 & "组解: " & s
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Form1.Cls
End Sub
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 楼主| 发表于 2021-2-16 09:11 | 显示全部楼层

已知a^2+b^2=c^2,且a+b=k问a、b、c有多少组正整数解并写出这些解?
解:a+b=k,令k有n个素因子,且每个素因子都能表示为勾股数的两个直角边,称这样的素因子为有效素因子。
通过试验,
当n=1时,单解数是1;
当n=2时,单解数是2;
当n=3时,单解数是4;
当n=4时,单解数是8;
当n=5时,单解数是16;
当n=6时,单解数是32;
…………………………
推断当a+b=k有n个有效素因子时,其单解数公式是=2^(n-1)
当n=1时,总解数是1;
当n=2时,总解数是4;
当n=3时,总解数是13;
当n=4时,总解数是40;
当n=5时,总解数是121;
当n=6时,总解数是364;
…………………………
总解数数列:1  4  13  40  121  364……
显然,前项乘以3再加上1得到后项。
推断当a+b=k有n个有效素因子时,其总解数公式是:G=(1/2)*(3^n -1)
也就是a、b、c正整数解的组数是:
C(n,1)*2^0+C(n,2)*2^1+C(n,3)*2^2+C(n,4)*2^3+C(n,5)*2^4+……+C(n,i)*2^(i-1)+……+C(n,n)*2^(n-1)=(1/2)*(3^n -1)
其中,C(n,i)表示从n个元素中取出i个元素的组合数。
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 楼主| 发表于 2021-2-16 09:18 | 显示全部楼层
推断当a+b=k有n个有效素因子时,其单解数公式是Q=2^(n-1)
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发表于 2021-2-16 09:24 | 显示全部楼层
猜想是对的,祝贺!!
新年快乐,万事如意!
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 楼主| 发表于 2021-2-16 09:24 | 显示全部楼层
ysr老师您好:您辛苦了!学生我衷心感谢!
总之,我们几个人联手终于攻克了一道数学题,为数论大厦添砖加瓦,我感到很欣慰。
老师,我们休息一下吧。
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发表于 2021-2-16 10:08 | 显示全部楼层
费尔马1 发表于 2021-2-16 01:24
ysr老师您好:您辛苦了!学生我衷心感谢!
总之,我们几个人联手终于攻克了一道数学题,为数论大厦添砖加瓦 ...

谢谢您,休息一下吧!

70071506*70071506=4910015953108036
93428663*93428663=8728915069967569
4910015953108036+8728915069967569=13638931023075605
116785834*116785834=13638931023075556

二者不相等,不符合勾股定理,不是勾股数解。改进一下程序就快了可能是。我试试能不能更快些。
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发表于 2021-2-16 11:16 | 显示全部楼层
快速程序出来了,9位以内的勾股数都可以,超过9位就失效了。对a+b=163500169验证了一下,几分钟就出来结果,结果是正确的,就是364组解。
代码如下;

Private Sub Command1_Click()
Dim x, Y, z
m = Text2
x = 1
Do While x < Val(m) / 2 + 1

Y = Val(m) - x
z = Sqr(x ^ 2 + Y ^ 2)
If InStr(z, ".") = 0 Then
If MPC(MPC1(MbC(Trim(x), Trim(x)), MbC(Trim(Y), Trim(Y))), MbC(Trim(z), Trim(z))) = 0 Then
s = s & "/解/" & x & "/" & Y & "/" & z
s1 = s1 + 1
Else
s1 = s1
End If

Else
s1 = s1
End If
x = x + 1
Loop

Text1 = Text1 & "有" & s1 & "组解: " & s
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""

End Sub










Public Function MbC(D1 As String, D2 As String) As String '乘法
Dim x, Y '两数长度
x = Len(D1): Y = Len(D2)
Dim a() As Integer
ReDim a(1 To x + Y, 1 To Y)
Dim I, J, C1, C2, CJ, JW
For J = Y To 1 Step -1 'D2
JW = 0 '进位清0
C2 = Mid$(D2, J, 1) '每位数
For I = x To 1 Step -1 'D1
  C1 = Mid$(D1, I, 1) '每位数
  CJ = C1 * C2 + JW '计算乘积
  c = I + J: r = Y + 1 - J
  a(c, r) = CJ Mod 10 '本位
  JW = CJ \ 10 '进位
Next
a(c - 1, r) = JW
Next
Dim b() As Integer
ReDim b(1 To x + Y)
JW = 0
For I = x + Y To 1 Step -1
Bit = JW
For J = 1 To Y
  Bit = Bit + a(I, J)
Next
b(I) = Bit Mod 10
JW = Bit \ 10
Next
If b(1) > 0 Then
MbC = MbC & b(1)
Else
MbC = MbC
End If
For I = 2 To x + Y
MbC = MbC & b(I)
Next
End Function

Public Function MPC(D1 As String, D2 As String) As String ';jianfaqi
Dim x, Y ';两数长度
If Len(D1) >= Len(D2) Then
D4 = String(Len(D1) - Len(D2), "0") & D2
d3 = D1
Else
D4 = D2
d3 = String(Len(D2) - Len(D1), "0") & D1
End If
x = Len(d3): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
ReDim a(1 To x)
ReDim B1(1 To Y)
ReDim C1(1 To x)
ReDim E1(1 To x)
Dim I, J, C2, CJ, JW
For J = Y To 1 Step -1 ';D2
JW = 1 ';yu jie weichuzhi
B1(J) = Mid(D4, J, 1) ';每位数
For I = x To 1 Step -1  ';D1
   a(I) = Mid(d3, I, 1) ';每位数
   C1(I) = 10 + a(I) - B1(I) - 1 + JW ';计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  Next
  Next
  For r = 1 To x
  MPC = MPC & E1(r)
  For I = 1 To Len(MPC)
    If Not Mid(MPC, I, 1) = "0" Then
        Exit For
    End If
Next
strtmp = Mid(MPC, I)
  If Len(strtmp) = 0 Then
  MPC = "0"
  Else
MPC = strtmp
End If
  Next
  
  
End Function
  Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
Dim x, Y '两数长度

If Len(D1) >= Len(D2) Then
D4 = String(Len(D1) - Len(D2), "0") & D2
d3 = D1
Else
D4 = D2
d3 = String(Len(D2) - Len(D1), "0") & D1
End If
x = Len(d3): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
ReDim a(1 To x)
ReDim B1(1 To Y)
ReDim C1(1 To x)
ReDim E1(1 To x)
Dim I, J, C2, CJ, JW
For J = Y To 1 Step -1 'D2
JW = 0 '进位清0
B1(J) = Mid$(D4, J, 1) '每位数
For I = x To 1 Step -1  'D1
   a(I) = Mid$(d3, I, 1) '每位数
   C1(I) = a(I) + B1(I) + JW '计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  Next
  Next
  For r = 1 To x
  If JW = 0 Then
  MPC1 = MPC1 & E1(r)
  Else
  jc = jc & E1(r)
  MPC1 = JW & jc
  End If
  Next
  
End Function


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发表于 2021-2-16 12:40 | 显示全部楼层
当a+b=2^n时没有勾股数解。
而a+b=100000001有4组解: /解/1980200/98019801/98039801/解/27873965/72126036/77324789/解/29411765/70588236/76470589/解/47437997/52562004/70803445

点评

ysr老师:您好!用您的程序算一算7*17*23*31*41的121组解好吗?  发表于 2021-2-16 17:43
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