Concatenation: 2016 || x || 2016 = y^2

Posted on February 2, 2016 by benvitalis

$\underline{2016}0459\underline{2016} \; = \; 449004^2$

$\underline{2016}904507\underline{2016} \; = \; 4490996^2$

$\underline{2016}1171459\underline{2016} \; = \; 14199004^2$

$\underline{2016}6828739\underline{2016} \; = \; 14200996^2$

$\underline{2016}8271586\underline{2016} \; = \; 14201504^2$

Find other solutions.

Also find $2016 \; || \; x \; || \; 2016 \; = \; y^3$

Paul found:

$\underline{2016}14506146\underline{2016} \; = \; 44901504^2$
$\underline{2016}32395302\underline{2016} \; = \; 44903496^2$
$\underline{2016}36957523\underline{2016} \; = \; 44904004^2$
$\underline{2016}54847675\underline{2016} \; = \; 44905996^2$
$\underline{2016}59410150\underline{2016} \; = \; 44906504^2$
$\underline{2016}77301298\underline{2016} \; = \; 44908496^2$
$\underline{2016}81864027\underline{2016} \; = \; 44909004^2$
$\underline{2016}99756171\underline{2016} \; = \; 44910996^2$

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7 Responses to Concatenation: 2016 || x || 2016 = y^2

paul says:

February 3, 2016 at 5:30 pm

Here are a few more

2016145061462016 = 44901504^2
2016323953022016 = 44903496^2
2016369575232016 = 44904004^2
2016548476752016 = 44905996^2
2016594101502016 = 44906504^2
2016773012982016 = 44908496^2
2016818640272016 = 44909004^2
2016997561712016 = 44910996^2

and a family of cubes

2016402567739822016 = 1263356^3
2016304889932064782016 = 12633356^3
2016295122324787314382016 = 126333356^3
2016294145565794539810382016 = 1263333356^3
etc, just keep adding another 3 into the cube

Paul.

Reply
- benvitalis says:
  
  February 3, 2016 at 5:48 pm
  
  Nice work!
  
  Reply
pipo says:

February 3, 2016 at 6:01 pm

A few more, 2016 appear every 2500 starting at 856

1263356^3 = 2016402567739822016
12633356^3 = 2016304889932064782016
27218356^3 = 20164417009832178462016
27220856^3 = 20169973811967048982016
58638356^3 = 201625453599633673822016
58640856^3 = 201651243125076344342016
58643356^3 = 201677034849551114862016
126328356^3 = 2016055730047090673342016
126330856^3 = 2016175423817235443862016
126333356^3 = 2016295122324787314382016
126335856^3 = 2016414825569840034902016
126338356^3 = 2016534533552487355422016
126340856^3 = 2016654246272823025942016
126343356^3 = 2016773963730940796462016
126345856^3 = 2016893685926934416982016
272165856^3 = 20160482522175994707542016
272168356^3 = 20161038084177911728062016
272170856^3 = 20161593656386142098582016
272173356^3 = 20162149238800779569102016
272175856^3 = 20162704831421917889622016
272178356^3 = 20163260434249650810142016
272180856^3 = 20163816047284072080662016
272183356^3 = 20164371670525275451182016
272185856^3 = 20164927303973354671702016
272188356^3 = 20165482947628403492222016
272190856^3 = 20166038601490515662742016
272193356^3 = 20166594265559784933262016
272195856^3 = 20167149939836305053782016
272198356^3 = 20167705624320169774302016
272200856^3 = 20168261319011472844822016
272203356^3 = 20168817023910308015342016
272205856^3 = 20169372739016769035862016
272208356^3 = 20169928464330949656382016
586360856^3 = 201602034489496314670102016
586363356^3 = 201604613143391464240622016
586365856^3 = 201607191819275239661142016
586368356^3 = 201609770517147734681662016
586370856^3 = 201612349237009043052182016
586373356^3 = 201614927978859258522702016
586375856^3 = 201617506742698474843222016
586378356^3 = 201620085528526785763742016
586380856^3 = 201622664336344285034262016
586383356^3 = 201625243166151066404782016
586385856^3 = 201627822017947223625302016
586388356^3 = 201630400891732850445822016
586390856^3 = 201632979787508040616342016
586393356^3 = 201635558705272887886862016
586395856^3 = 201638137645027486007382016
586398356^3 = 201640716606771928727902016
586400856^3 = 201643295590506309798422016
586403356^3 = 201645874596230722968942016
586405856^3 = 201648453623945261989462016
586408356^3 = 201651032673650020609982016
586410856^3 = 201653611745345092580502016
586413356^3 = 201656190839030571651022016
586415856^3 = 201658769954706551571542016
586418356^3 = 201661349092373126092062016
586420856^3 = 201663928252030388962582016
586423356^3 = 201666507433678433933102016
586425856^3 = 201669086637317354753622016
586428356^3 = 201671665862947245174142016
586430856^3 = 201674245110568198944662016
586433356^3 = 201676824380180309815182016
586435856^3 = 201679403671783671535702016
586438356^3 = 201681982985378377856222016
586440856^3 = 201684562320964522526742016
586443356^3 = 201687141678542199297262016
586445856^3 = 201689721058111501917782016
586448356^3 = 201692300459672524138302016
586450856^3 = 201694879883225359708822016
586453356^3 = 201697459328770102379342016
1263273356^3 = 2016006877199269984517902016
1263275856^3 = 2016018846169746221838422016
1263278356^3 = 2016030815187595303758942016
1263280856^3 = 2016042784252817324029462016
1263283356^3 = 2016054753365412376399982016
1263285856^3 = 2016066722525380554620502016
1263288356^3 = 2016078691732721952441022016
1263290856^3 = 2016090660987436663611542016
1263293356^3 = 2016102630289524781882062016
1263295856^3 = 2016114599638986401002582016
1263298356^3 = 2016126569035821614723102016
1263300856^3 = 2016138538480030516793622016
1263303356^3 = 2016150507971613200964142016
1263305856^3 = 2016162477510569760984662016
1263308356^3 = 2016174447096900290605182016
1263310856^3 = 2016186416730604883575702016
1263313356^3 = 2016198386411683633646222016
1263315856^3 = 2016210356140136634566742016
1263318356^3 = 2016222325915963980087262016
1263320856^3 = 2016234295739165763957782016
1263323356^3 = 2016246265609742079928302016
1263325856^3 = 2016258235527693021748822016
1263328356^3 = 2016270205493018683169342016
1263330856^3 = 2016282175505719157939862016
1263333356^3 = 2016294145565794539810382016
1263335856^3 = 2016306115673244922530902016
1263338356^3 = 2016318085828070399851422016
1263340856^3 = 2016330056030271065521942016
1263343356^3 = 2016342026279847013292462016
1263345856^3 = 2016353996576798336912982016
1263348356^3 = 2016365966921125130133502016
1263350856^3 = 2016377937312827486704022016
1263353356^3 = 2016389907751905500374542016
1263355856^3 = 2016401878238359264895062016
1263358356^3 = 2016413848772188874015582016
1263360856^3 = 2016425819353394421486102016
1263363356^3 = 2016437789981976001056622016
1263365856^3 = 2016449760657933706477142016
1263368356^3 = 2016461731381267631497662016
1263370856^3 = 2016473702151977869868182016
1263373356^3 = 2016485672970064515338702016
1263375856^3 = 2016497643835527661659222016
1263378356^3 = 2016509614748367402579742016
1263380856^3 = 2016521585708583831850262016
1263383356^3 = 2016533556716177043220782016
1263385856^3 = 2016545527771147130441302016
1263388356^3 = 2016557498873494187261822016
1263390856^3 = 2016569470023218307432342016
1263393356^3 = 2016581441220319584702862016
1263395856^3 = 2016593412464798112823382016
1263398356^3 = 2016605383756653985543902016
1263400856^3 = 2016617355095887296614422016
1263403356^3 = 2016629326482498139784942016
1263405856^3 = 2016641297916486608805462016
1263408356^3 = 2016653269397852797425982016
1263410856^3 = 2016665240926596799396502016
1263413356^3 = 2016677212502718708467022016
1263415856^3 = 2016689184126218618387542016
1263418356^3 = 2016701155797096622908062016
1263420856^3 = 2016713127515352815778582016
1263423356^3 = 2016725099280987290749102016
1263425856^3 = 2016737071094000141569622016
1263428356^3 = 2016749042954391461990142016
1263430856^3 = 2016761014862161345760662016
1263433356^3 = 2016772986817309886631182016
1263435856^3 = 2016784958819837178351702016
1263438356^3 = 2016796930869743314672222016
1263440856^3 = 2016808902967028389342742016
1263443356^3 = 2016820875111692496113262016
1263445856^3 = 2016832847303735728733782016
1263448356^3 = 2016844819543158180954302016
1263450856^3 = 2016856791829959946524822016
1263453356^3 = 2016868764164141119195342016
1263455856^3 = 2016880736545701792715862016
1263458356^3 = 2016892708974642060836382016
1263460856^3 = 2016904681450962017306902016
1263463356^3 = 2016916653974661755877422016
1263465856^3 = 2016928626545741370297942016
1263468356^3 = 2016940599164200954318462016
1263470856^3 = 2016952571830040601688982016
1263473356^3 = 2016964544543260406159502016
1263475856^3 = 2016976517303860461480022016
1263478356^3 = 2016988490111840861400542016
2721638356^3 = 20160033546645615311577822016
2721640856^3 = 20160089101561702424248342016
2721643356^3 = 20160144656579851069018862016
2721645856^3 = 20160200211700061339639382016
2721648356^3 = 20160255766922333329859902016
2721650856^3 = 20160311322246667133430422016
2721653356^3 = 20160366877673062844100942016
2721655856^3 = 20160422433201520555621462016
2721658356^3 = 20160477988832040361741982016
2721660856^3 = 20160533544564622356212502016
2721663356^3 = 20160589100399266632783022016
2721665856^3 = 20160644656335973285203542016
2721668356^3 = 20160700212374742407224062016
2721670856^3 = 20160755768515574092594582016
2721673356^3 = 20160811324758468435065102016
2721675856^3 = 20160866881103425528385622016
2721678356^3 = 20160922437550445466306142016
2721680856^3 = 20160977994099528342576662016
2721683356^3 = 20161033550750674250947182016
2721685856^3 = 20161089107503883285167702016
2721688356^3 = 20161144664359155538988222016
2721690856^3 = 20161200221316491106158742016
2721693356^3 = 20161255778375890080429262016
2721695856^3 = 20161311335537352555549782016
2721698356^3 = 20161366892800878625270302016
2721700856^3 = 20161422450166468383340822016
2721703356^3 = 20161478007634121923511342016
2721705856^3 = 20161533565203839339531862016
2721708356^3 = 20161589122875620725152382016
2721710856^3 = 20161644680649466174122902016
2721713356^3 = 20161700238525375780193422016
2721715856^3 = 20161755796503349637113942016
2721718356^3 = 20161811354583387838634462016
2721720856^3 = 20161866912765490478504982016
2721723356^3 = 20161922471049657650475502016
2721725856^3 = 20161978029435889448296022016
2721728356^3 = 20162033587924185965716542016
2721730856^3 = 20162089146514547296487062016
2721733356^3 = 20162144705206973534357582016
2721735856^3 = 20162200264001464773078102016
2721738356^3 = 20162255822898021106398622016
2721740856^3 = 20162311381896642628069142016
2721743356^3 = 20162366940997329431839662016
2721745856^3 = 20162422500200081611460182016
2721748356^3 = 20162478059504899260680702016
2721750856^3 = 20162533618911782473251222016
2721753356^3 = 20162589178420731342921742016
2721755856^3 = 20162644738031745963442262016
2721758356^3 = 20162700297744826428562782016
2721760856^3 = 20162755857559972832033302016
2721763356^3 = 20162811417477185267603822016
2721765856^3 = 20162866977496463829024342016
2721768356^3 = 20162922537617808610044862016
2721770856^3 = 20162978097841219704415382016
2721773356^3 = 20163033658166697205885902016
2721775856^3 = 20163089218594241208206422016
2721778356^3 = 20163144779123851805126942016
2721780856^3 = 20163200339755529090397462016
2721783356^3 = 20163255900489273157767982016
2721785856^3 = 20163311461325084100988502016
2721788356^3 = 20163367022262962013809022016
2721790856^3 = 20163422583302906989979542016
2721793356^3 = 20163478144444919123250062016
2721795856^3 = 20163533705688998507370582016
2721798356^3 = 20163589267035145236091102016
2721800856^3 = 20163644828483359403161622016
2721803356^3 = 20163700390033641102332142016
2721805856^3 = 20163755951685990427352662016
2721808356^3 = 20163811513440407471973182016
2721810856^3 = 20163867075296892329943702016
2721813356^3 = 20163922637255445095014222016
2721815856^3 = 20163978199316065860934742016
2721818356^3 = 20164033761478754721455262016
2721820856^3 = 20164089323743511770325782016
2721823356^3 = 20164144886110337101296302016
2721825856^3 = 20164200448579230808116822016
2721828356^3 = 20164256011150192984537342016
2721830856^3 = 20164311573823223724307862016
2721833356^3 = 20164367136598323121178382016
2721835856^3 = 20164422699475491268898902016
2721838356^3 = 20164478262454728261219422016
2721840856^3 = 20164533825536034191889942016
2721843356^3 = 20164589388719409154660462016
2721845856^3 = 20164644952004853243280982016
2721848356^3 = 20164700515392366551501502016
2721850856^3 = 20164756078881949173072022016
2721853356^3 = 20164811642473601201742542016
2721855856^3 = 20164867206167322731263062016
2721858356^3 = 20164922769963113855383582016
2721860856^3 = 20164978333860974667854102016
2721863356^3 = 20165033897860905262424622016
2721865856^3 = 20165089461962905732845142016
2721868356^3 = 20165145026166976172865662016
2721870856^3 = 20165200590473116676236182016
2721873356^3 = 20165256154881327336706702016
2721875856^3 = 20165311719391608248027222016
2721878356^3 = 20165367284003959503947742016
2721880856^3 = 20165422848718381198218262016
2721883356^3 = 20165478413534873424588782016
2721885856^3 = 20165533978453436276809302016
2721888356^3 = 20165589543474069848629822016
2721890856^3 = 20165645108596774233800342016
2721893356^3 = 20165700673821549526070862016
2721895856^3 = 20165756239148395819191382016
2721898356^3 = 20165811804577313206911902016
2721900856^3 = 20165867370108301782982422016
2721903356^3 = 20165922935741361641152942016
2721905856^3 = 20165978501476492875173462016
2721908356^3 = 20166034067313695578793982016
2721910856^3 = 20166089633252969845764502016
2721913356^3 = 20166145199294315769835022016
2721915856^3 = 20166200765437733444755542016
2721918356^3 = 20166256331683222964276062016
2721920856^3 = 20166311898030784422146582016
2721923356^3 = 20166367464480417912117102016
2721925856^3 = 20166423031032123527937622016
2721928356^3 = 20166478597685901363358142016
2721930856^3 = 20166534164441751512128662016
2721933356^3 = 20166589731299674067999182016
2721935856^3 = 20166645298259669124719702016
2721938356^3 = 20166700865321736776040222016
2721940856^3 = 20166756432485877115710742016
2721943356^3 = 20166811999752090237481262016
2721945856^3 = 20166867567120376235101782016
2721948356^3 = 20166923134590735202322302016
2721950856^3 = 20166978702163167232892822016
2721953356^3 = 20167034269837672420563342016
2721955856^3 = 20167089837614250859083862016
2721958356^3 = 20167145405492902642204382016
2721960856^3 = 20167200973473627863674902016
2721963356^3 = 20167256541556426617245422016
2721965856^3 = 20167312109741298996665942016
2721968356^3 = 20167367678028245095686462016
2721970856^3 = 20167423246417265008056982016
2721973356^3 = 20167478814908358827527502016
2721975856^3 = 20167534383501526647848022016
2721978356^3 = 20167589952196768562768542016
2721980856^3 = 20167645520994084666039062016
2721983356^3 = 20167701089893475051409582016
2721985856^3 = 20167756658894939812630102016
2721988356^3 = 20167812227998479043450622016
2721990856^3 = 20167867797204092837621142016
2721993356^3 = 20167923366511781288891662016
2721995856^3 = 20167978935921544491012182016
2721998356^3 = 20168034505433382537732702016
2722000856^3 = 20168090075047295522803222016
2722003356^3 = 20168145644763283539973742016
2722005856^3 = 20168201214581346682994262016
2722008356^3 = 20168256784501485045614782016
2722010856^3 = 20168312354523698721585302016
2722013356^3 = 20168367924647987804655822016
2722015856^3 = 20168423494874352388576342016
2722018356^3 = 20168479065202792567096862016
2722020856^3 = 20168534635633308433967382016
2722023356^3 = 20168590206165900082937902016
2722025856^3 = 20168645776800567607758422016
2722028356^3 = 20168701347537311102178942016
2722030856^3 = 20168756918376130659949462016
2722033356^3 = 20168812489317026374819982016
2722035856^3 = 20168868060359998340540502016
2722038356^3 = 20168923631505046650861022016
2722040856^3 = 20168979202752171399531542016
2722043356^3 = 20169034774101372680302062016
2722045856^3 = 20169090345552650586922582016
2722048356^3 = 20169145917106005213143102016
2722050856^3 = 20169201488761436652713622016
2722053356^3 = 20169257060518944999384142016
2722055856^3 = 20169312632378530346904662016
2722058356^3 = 20169368204340192789025182016
2722060856^3 = 20169423776403932419495702016
2722063356^3 = 20169479348569749332066222016
2722065856^3 = 20169534920837643620486742016
2722068356^3 = 20169590493207615378507262016
2722070856^3 = 20169646065679664699877782016
2722073356^3 = 20169701638253791678348302016
2722075856^3 = 20169757210929996407668822016
2722078356^3 = 20169812783708278981589342016
2722080856^3 = 20169868356588639493859862016
2722083356^3 = 20169923929571078038230382016
2722085856^3 = 20169979502655594708450902016
5863590856^3 = 201600208403253151431873942016
5863593356^3 = 201600466266096043027144462016
5863595856^3 = 201600724129158819373264982016
5863598356^3 = 201600981992441480563985502016
5863600856^3 = 201601239855944026693056022016
5863603356^3 = 201601497719666457854226542016
5863605856^3 = 201601755583608774141247062016
5863608356^3 = 201602013447770975647867582016
5863610856^3 = 201602271312153062467838102016
5863613356^3 = 201602529176755034694908622016
5863615856^3 = 201602787041576892422829142016
5863618356^3 = 201603044906618635745349662016
5863620856^3 = 201603302771880264756220182016
5863623356^3 = 201603560637361779549190702016
5863625856^3 = 201603818503063180218011222016
5863628356^3 = 201604076368984466856431742016
5863630856^3 = 201604334235125639558202262016
5863633356^3 = 201604592101486698417072782016
5863635856^3 = 201604849968067643526793302016
5863638356^3 = 201605107834868474981113822016
5863640856^3 = 201605365701889192873784342016
5863643356^3 = 201605623569129797298554862016
5863645856^3 = 201605881436590288349175382016
5863648356^3 = 201606139304270666119395902016
5863650856^3 = 201606397172170930702966422016
5863653356^3 = 201606655040291082193636942016
5863655856^3 = 201606912908631120685157462016
5863658356^3 = 201607170777191046271277982016
5863660856^3 = 201607428645970859045748502016
5863663356^3 = 201607686514970559102319022016
5863665856^3 = 201607944384190146534739542016
5863668356^3 = 201608202253629621436760062016
5863670856^3 = 201608460123288983902130582016
5863673356^3 = 201608717993168234024601102016
5863675856^3 = 201608975863267371897921622016
5863678356^3 = 201609233733586397615842142016
5863680856^3 = 201609491604125311272112662016
5863683356^3 = 201609749474884112960483182016
5863685856^3 = 201610007345862802774703702016
5863688356^3 = 201610265217061380808524222016
5863690856^3 = 201610523088479847155694742016
5863693356^3 = 201610780960118201909965262016
5863695856^3 = 201611038831976445165085782016
5863698356^3 = 201611296704054577014806302016
5863700856^3 = 201611554576352597552876822016
5863703356^3 = 201611812448870506873047342016
5863705856^3 = 201612070321608305069067862016
5863708356^3 = 201612328194565992234688382016
5863710856^3 = 201612586067743568463658902016
5863713356^3 = 201612843941141033849729422016
5863715856^3 = 201613101814758388486649942016
5863718356^3 = 201613359688595632468170462016
5863720856^3 = 201613617562652765888040982016
5863723356^3 = 201613875436929788840011502016
5863725856^3 = 201614133311426701417832022016
5863728356^3 = 201614391186143503715252542016
5863730856^3 = 201614649061080195826023062016
5863733356^3 = 201614906936236777843893582016
5863735856^3 = 201615164811613249862614102016
5863738356^3 = 201615422687209611975934622016
5863740856^3 = 201615680563025864277605142016
5863743356^3 = 201615938439062006861375662016
5863745856^3 = 201616196315318039820996182016
5863748356^3 = 201616454191793963250216702016
5863750856^3 = 201616712068489777242787222016
5863753356^3 = 201616969945405481892457742016
5863755856^3 = 201617227822541077292978262016
5863758356^3 = 201617485699896563538098782016
5863760856^3 = 201617743577471940721569302016
5863763356^3 = 201618001455267208937139822016
5863765856^3 = 201618259333282368278560342016
5863768356^3 = 201618517211517418839580862016
5863770856^3 = 201618775089972360713951382016
5863773356^3 = 201619032968647193995421902016
5863775856^3 = 201619290847541918777742422016
5863778356^3 = 201619548726656535154662942016
5863780856^3 = 201619806605991043219933462016
5863783356^3 = 201620064485545443067303982016
5863785856^3 = 201620322365319734790524502016
5863788356^3 = 201620580245313918483345022016
5863790856^3 = 201620838125527994239515542016
5863793356^3 = 201621096005961962152786062016
5863795856^3 = 201621353886615822316906582016
5863798356^3 = 201621611767489574825627102016
5863800856^3 = 201621869648583219772697622016
5863803356^3 = 201622127529896757251868142016
5863805856^3 = 201622385411430187356888662016
5863808356^3 = 201622643293183510181509182016
5863810856^3 = 201622901175156725819479702016
5863813356^3 = 201623159057349834364550222016
5863815856^3 = 201623416939762835910470742016
5863818356^3 = 201623674822395730550991262016
5863820856^3 = 201623932705248518379861782016
5863823356^3 = 201624190588321199490832302016
5863825856^3 = 201624448471613773977652822016
5863828356^3 = 201624706355126241934073342016
5863830856^3 = 201624964238858603453843862016
5863833356^3 = 201625222122810858630714382016
5863835856^3 = 201625480006983007558434902016
5863838356^3 = 201625737891375050330755422016
5863840856^3 = 201625995775986987041425942016
5863843356^3 = 201626253660818817784196462016
5863845856^3 = 201626511545870542652816982016
5863848356^3 = 201626769431142161741037502016
5863850856^3 = 201627027316633675142608022016
5863853356^3 = 201627285202345082951278542016
5863855856^3 = 201627543088276385260799062016
5863858356^3 = 201627800974427582164919582016
5863860856^3 = 201628058860798673757390102016
5863863356^3 = 201628316747389660131960622016
5863865856^3 = 201628574634200541382381142016
5863868356^3 = 201628832521231317602401662016
5863870856^3 = 201629090408481988885772182016
5863873356^3 = 201629348295952555326242702016
5863875856^3 = 201629606183643017017563222016
5863878356^3 = 201629864071553374053483742016
5863880856^3 = 201630121959683626527754262016
5863883356^3 = 201630379848033774534124782016
5863885856^3 = 201630637736603818166345302016
5863888356^3 = 201630895625393757518165822016
5863890856^3 = 201631153514403592683336342016
5863893356^3 = 201631411403633323755606862016
5863895856^3 = 201631669293082950828727382016
5863898356^3 = 201631927182752473996447902016
5863900856^3 = 201632185072641893352518422016
5863903356^3 = 201632442962751208990688942016
5863905856^3 = 201632700853080421004709462016
5863908356^3 = 201632958743629529488329982016
5863910856^3 = 201633216634398534535300502016
5863913356^3 = 201633474525387436239371022016
5863915856^3 = 201633732416596234694291542016
5863918356^3 = 201633990308024929993812062016
5863920856^3 = 201634248199673522231682582016
5863923356^3 = 201634506091542011501653102016
5863925856^3 = 201634763983630397897473622016
5863928356^3 = 201635021875938681512894142016
5863930856^3 = 201635279768466862441664662016
5863933356^3 = 201635537661214940777535182016
5863935856^3 = 201635795554182916614255702016
5863938356^3 = 201636053447370790045576222016
5863940856^3 = 201636311340778561165246742016
5863943356^3 = 201636569234406230067017262016
5863945856^3 = 201636827128253796844637782016
5863948356^3 = 201637085022321261591858302016
5863950856^3 = 201637342916608624402428822016
5863953356^3 = 201637600811115885370099342016
5863955856^3 = 201637858705843044588619862016
5863958356^3 = 201638116600790102151740382016
5863960856^3 = 201638374495957058153210902016
5863963356^3 = 201638632391343912686781422016
5863965856^3 = 201638890286950665846201942016
5863968356^3 = 201639148182777317725222462016
5863970856^3 = 201639406078823868417592982016
5863973356^3 = 201639663975090318017063502016
5863975856^3 = 201639921871576666617384022016
5863978356^3 = 201640179768282914312304542016
5863980856^3 = 201640437665209061195575062016
5863983356^3 = 201640695562355107360945582016
5863985856^3 = 201640953459721052902166102016
5863988356^3 = 201641211357306897912986622016
5863990856^3 = 201641469255112642487157142016
5863993356^3 = 201641727153138286718427662016
5863995856^3 = 201641985051383830700548182016
5863998356^3 = 201642242949849274527268702016
5864000856^3 = 201642500848534618292339222016
5864003356^3 = 201642758747439862089509742016
5864005856^3 = 201643016646565006012530262016
5864008356^3 = 201643274545910050155150782016
5864010856^3 = 201643532445474994611121302016
5864013356^3 = 201643790345259839474191822016
5864015856^3 = 201644048245264584838112342016
5864018356^3 = 201644306145489230796632862016
5864020856^3 = 201644564045933777443503382016
5864023356^3 = 201644821946598224872473902016
5864025856^3 = 201645079847482573177294422016
5864028356^3 = 201645337748586822451714942016
5864030856^3 = 201645595649910972789485462016
5864033356^3 = 201645853551455024284355982016
5864035856^3 = 201646111453218977030076502016
5864038356^3 = 201646369355202831120397022016
5864040856^3 = 201646627257406586649067542016
5864043356^3 = 201646885159830243709838062016
5864045856^3 = 201647143062473802396458582016
5864048356^3 = 201647400965337262802679102016
5864050856^3 = 201647658868420625022249622016
5864053356^3 = 201647916771723889148920142016
5864055856^3 = 201648174675247055276440662016

Reply
- benvitalis says:
  
  February 3, 2016 at 6:04 pm
  
  Good catch!
  
  Reply
pipo says:

February 3, 2016 at 6:13 pm

And here some fourth powers, fifth powers are not possible:

670136^4 = 201674874895868164182016
2118998^4 = 20161469688819491796192016
3768502^4 = 201685650585204053834592016
6701002^4 = 2016317828549399489838432016
6701114^4 = 2016452634214914363850272016
6701386^4 = 2016780047544421342446432016
6701498^4 = 2016914876386131077739552016
11916002^4 = 20161473519721930153725312016
11916114^4 = 20162231531300124175138112016
11916386^4 = 20164072505548042598558592016
11916498^4 = 20164830590410327596452672016
11917252^4 = 20169934682357835605754102016
21189752^4 = 201606019690956696446580822016
21189864^4 = 201610282138809301503891542016
21190136^4 = 201620634079270719923992662016
21190248^4 = 201624896758858738133784662016
21191002^4 = 201653595486024305372222112016
21191114^4 = 201657858688254787872220512016
21191386^4 = 201668212460809965442476192016
21191498^4 = 201672475894803202086955872016
37681114^4 = 2016020458339741434972142752016
37681386^4 = 2016078669304751771381353952016
37681498^4 = 2016102638892036305404908192016
37682252^4 = 2016264011140768783288398582016
37682364^4 = 2016287982380708195602559222016
37682636^4 = 2016346199139007242911924982016
37682748^4 = 2016370171111787908455366902016
37683502^4 = 2016531559420390207034839872016
37683614^4 = 2016555533045935397900088192016
37683886^4 = 2016613755597907517609608512016
37683998^4 = 2016637729956342581979338112016
37684752^4 = 2016799134325880191614168662016
37684864^4 = 2016823110337189431974104662016
37685136^4 = 2016881338683218998333779542016
37685248^4 = 2016905315427466734086196822016
67007636^4 = 20160309075672359968902913782016
67007748^4 = 20160443863909185596703328502016
67008502^4 = 20161351295166070666315378272016
67008614^4 = 20161486088628928627505599392016
67008886^4 = 20161813446995514004841097312016
67008998^4 = 20161948242775732072111799712016
67009752^4 = 20162855724816468984654207062016
67009864^4 = 20162990525822914364695115862016
67010136^4 = 20163317902509745601180768342016
67010248^4 = 20163452705833637545478158422016
67011002^4 = 20164360238660120991029048352016
67011114^4 = 20164495047210435231114244832016
67011386^4 = 20164822442218195828750051872016
67011498^4 = 20164957253086043092880529632016
67012252^4 = 20165864836700167796861777142016
67012364^4 = 20165999652794632343434861302016
67012636^4 = 20166327066124005816970822902016
67012748^4 = 20166461884536089848990788342016
67013502^4 = 20167369518939750572168018432016
67013614^4 = 20167504342578646876922590272016
67013886^4 = 20167831774230316753858706432016
67013998^4 = 20167966600186919007074559552016
67014752^4 = 20168874285382010545557147222016
67014864^4 = 20169009116565620065436806742016
67015136^4 = 20169336566540269886023077462016
67015248^4 = 20169471400041671818991218262016

pipo

Reply
- paul says:
  
  February 3, 2016 at 7:36 pm
  
  We would have to wait while 2576 before it would work for 5th powers.
  
  Reply
pipo says:

February 3, 2016 at 8:41 pm

I think till 2032.
(152 mod 250)^5 = 2032 mod 10000.
According to me first is:
182652^5 = 203292876055102470906412032

Reply

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