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1000th digit (Posted on 2005-04-26) Difficulty: 3 of 5
What is the 1000th digit to the right of the decimal point in the decimal representation of (1+√2)^3000?

This problem can be solved by algebra alone, without the need for computers or calculators

See The Solution Submitted by Pemmadu Raghu Ramaiah    
Rating: 3.3750 (8 votes)

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Here Jonathan! | Comment 17 of 30 |

They say don't feed the trolls but chew on this (the 1000th 9 is in boldface):

2123518327356612118500367213758867765414197418468
30798047797649326633830265800348754922726611482329
69697838694171238662831323372232939683172926297627
19359130289686862178541716944797509500071385987020
47874928937006048825941728804726445558472950595484
37240825880525597396389361256574465945258888563467
22511246949612678048981527958151023832849470730211
58623268979166708897371716288813328574125896002105
52234253126450066766601059300480564120140748552336
96611232703093217213199904256095862158912163795231
04027105154328230715943028688427964504737016740719
70564800476003347743906012082205640185684266484349
82647577321969365793802064187209520068656125622104
12207828131451616365295898234402537336762320382508
75492120282575480740455782000705512110264515684212
60645263015500335037103262435806862023436892903856
12858013208292479048892324242891437926936379579771
66127121967706439612073980330923050298135568848490
71324711360238541010137065802431153627386479397481
23348684831357244274136458378908357255958491925980
35658874387649777921963640787328594520201635930729
89854129015044899752807431821864984905798240573491
40600741150807126892554341838245583515532450000001.
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999952
90834144837284284939995002857160070297682460462236
42942779547405733289828412546046116083818053025319
89889631310800921145954922295992301756007360554085
48895569673171122695490685295191183704846853614459
60507491910511846886973363595835012870632906762166
45166351157543266626388116876585719731331197052231
86875402306411942600693603429814957455137766487964
98718219012601496816456849757593273683146512236212
54500537951208965100792431466409979782139882182850
24705901784445094065503597948178135072021116246547
70556800613338455029215890671255934974207964241668
19501844592466295996556219629673384496173838167848
69254254320722769506821000321978402288692604576960
99026749913449827081047414371433263868298395956797
45526172546953728450596519400061309003146391558813
70116622380385455525427417422899321871447189290515
52387773317585937648904018057478244442545420225067
82114300989372298134926934977229380162471645845385
55901978504130474066877573546258171596040295349333
18928788931859539395004939997145908979182142820171
16573109943277311990922615411872725506226333087804
74923601801159796565776852574786524718812325486158
94325830050825905845912139198869843417674774837624
93042232189898553737650916095742112660492766407033
67428701553533242376799124244468943807984536274460
81939396573705238251775230980265907915440665237415
69850850147219096490013130679099923154092416542948
26831055131601082224615432052619730301621770982168
56247176352207397958239241231871821569326611821981
88458636326758234547981397686352078217855017370992
55678130706490968414716843713477698992400919967945
17510494639020713250787348309132980929193004789220
39915049981436775069764631294555244427773656775976
03387415165182547717297735536527214081674461277655
53410873994802854118160395829553403926224281865443
29059791044752703188305422093450163231755612499214
83512794120337429960937708228531981596787678664948
44397531010696720313974285990207251175069521095868
11753877365473738437413681941890377760268424324761
75595039494318375878866802873537709203449155287088
11198251818371851029661840090187022888827075645636
24506934179688750974857511926101243807641478411329
08558756862177452706827306126455496641168630894666
22478743244436653433178481826483083048436331930924
57741108759147340711898447111036284688705080156462
82485149809616792641938750355714443313217387292164
32886617116424246356160258827442185578874178677427
43992728956232370743270863365269964744396529799909
59870468883087935103091157656213905189751181148450
17328007206672329308926448875623703831487621065651
60784833951237648683236579058733540618052279778526
20934647077420189135576182733508011596794620086694
11252982867351050248513611140643392733756156600539
06677176443487974258969905353990822101427209719986
00970125659718571045960552024434230331691149068317
17669923691937498746514343243989152909854286440152
19568835710624315156042344799435403740104448278759
06951869713900296056472435575736820957367083596433
86604961879159591101022493029724871860860323968750
75633727379794126319603037426584501149724311520363
99450959300466886484598045130979537004009884730773
30798560010053629476619514538755443764295917849616
68157830281796720990846089269488796526115192131800
56895053632903445357155274100126592175720090757903
10821506780991491798633367144883124248113401682966
33757648404538490354775227358616230432279588820313
19850581587593910988994823024956463500970613370112
43907210296500186229421792383023377264860966186686
08083890012636831784419650071828123609406707306757
66143965985114574210636572735201962384270314065084
05404360514882766193439633178640694180689123818982
06663391313431780649585874355514218066868098908659
78788990973516099019458503062398777341706785003914
49536866536493636180796398661615643724327349374407
65194261933428434279563653052899021104401739843783
44406723756497149422335177363501501149178820324517
94386512877062932508212231112281293772591549017335
39581488526189218722594890009036036525565509747452
33891260728412091686274766728681377274547460744768
33636920820654649306975924065424113438754020865447
92912868528618563591462542740409855458812238236937
25299318022518008046374972736597354065339564196863
24571185535147814187336554183636418848468522320411
30856617790606193649310286343690219675394604529273
42723049681535911413151097166365629566921487309453
97475828024665134641836586135984872931033936648414
30700804393164643964868396302353744024575223483303
98752816973839168231376279758400203085889028602706
53653062576412742622945750513090397074942165168685
31277037250947091971769809294889861096611546926030
99453348502833121564233690143849578367953397754643
18789740145015277474348989730481621933701717764790
93072020304552389649084214036762476658780418124918
69438689322436594339972409309209286297017598733078
57194678781173743215818025795113062196301331057129
91132852347058192511385485081531600713466762771287
24411976037648283400404693765894371192816397411640
76516970828814081688882027524162129522551902984510
11936315111400040771876392217302713249081572579006
54656927651663822620880100946310870507900448433478
67043040641486611062194455824114704881746049057494
16562430372712953732640118086976074445793388477758
29417028870413634619741967156861735944196870990965
79371820897562204569025042846371911945410230696759
67971766166707628088362796054460573631271924482656
53408536108062561859885315143484317374751313974576
58496171712563134634948200628015852430951773981816
31699261187760579600673613773872060851981568751881
96477304187038687706848302452605179535096527952784
34666275683722409603603317760496491201888996845070
40809758812575148816668079795166231393061869662632
29221594548662348004957951539858819946546149418838
65451592233441619817507703796030856262727868434986
91318980678032937194119938320695544173819890497812
92644925239223601106882307791120550050050112015632
74696198729609240703818474209119050499284327972365
61102768768714641363499145366444699368424218266164
79275067940587065210425734619475084377879656713448
32188770784962980632863151011021210830537083321853
17175853455981893433902796993844629201831272317824
95219165417056940814348196312198642608377050232531
38223772976912800087663494157014706519809572783107
57025498039921621833762432999469183696078932000291
26828805890833954830156359829592035981119049266750
74349947646257014003390668776278166337541550187547
24712226918901738624952921593299821385859689919827
74651408651928927151379561859228790064617109794007
50722656485747723684899113830139788272312442697122
55113101914710725068421983927492416367690542850468
44121954307867870444437727446532524951911096472245
13107977669229399571925967567377734945897579914733
60569570677502483140703411273724284068563608730319
74021956055492985632183139167601535583905943681147
23316311497649489542308957617101250935452755910213
24114525777158579329655319675537192091231867195303
69627889052275944905739080522192787226032281865446
40678193541766142422705962018731192905323884029563
74086271170663801865259178723790593615562622957037
48109926999717490210030155911117430298497738551948
21231062434106902999543488075211827093325656316349
82155077776419480529646421720502634459863180116386
88279640696065372288860020089591492017164972999907
80276743276881992868361939235330702299757238071994
56635638987515251632962523828547018290766353812397
75709318561845661941567548829974484540031195163390
71797409519765473670952293349610803247696698025319
49482054507791516413990122853271666960489666863365
66197582081134799763301953697426355043109334996015
11082508231234442335591588674417755563821799755667
81527088585989442950814143412034532297790931867699
23882743299345922564361976924468667919254783585146
64208347733164117068845831709503672617483835269209
87062261538811815577732562547661769661554381072999
05005962100421312081702237817222942695596903479394
139178

I love using MIRACL Calc


  Posted by Jer on 2005-04-27 17:48:26
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