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 1000th digit (Posted on 2005-04-26)
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, you count 'em | Comment 16 of 30 |
212351832735661211850036721375886776541419741846830798047797649326633830265800348754922726611482329696978386941712386628313233722329396831729262976271935913028968686217854171694479750950007138598702047874928937006048825941728804726445558472950595484372408258805255973963893612565744659452588885634672251124694961267804898152795815102383284947073021158623268979166708897371716288813328574125896002105522342531264500667666010593004805641201407485523369661123270309321721319990425609586215891216379523104027105154328230715943028688427964504737016740719705648004760033477439060120822056401856842664843498264757732196936579380206418720952006865612562210412207828131451616365295898234402537336762320382508754921202825754807404557820007055121102645156842126064526301550033503710326243580686202343689290385612858013208292479048892324242891437926936379579771661271219677064396120739803309230502981355688484907132471136023854101013706580243115362738647939748123348684831357244274136458378908357255958491925980356588743876497779219636407873285945202016359307298985412901504489975280743182186498490579824057349140600741150807126892554341838245583515532450000001.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999952908341448372842849399950028571600702976824604622364294277954740573328982841254604611608381805302531989889631310800921145954922295992301756007360554085488955696731711226954906852951911837048468536144596050749191051184688697336359583501287063290676216645166351157543266626388116876585719731331197052231868754023064119426006936034298149574551377664879649871821901260149681645684975759327368314651223621254500537951208965100792431466409979782139882182850247059017844450940655035979481781350720211162465477055680061333845502921589067125593497420796424166819501844592466295996556219629673384496173838167848692542543207227695068210003219784022886926045769609902674991344982708104741437143326386829839595679745526172546953728450596519400061309003146391558813701166223803854555254274174228993218714471892905155238777331758593764890401805747824444254542022506782114300989372298134926934977229380162471645845385559019785041304740668775735462581715960402953493331892878893185953939500493999714590897918214282017116573109943277311990922615411872725506226333087804749236018011597965657768525747865247188123254861589432583005082590584591213919886984341767477483762493042232189898553737650916095742112660492766407033674287015535332423767991242444689438079845362744608193939657370523825177523098026590791544066523741569850850147219096490013130679099923154092416542948268310551316010822246154320526197303016217709821685624717635220739795823924123187182156932661182198188458636326758234547981397686352078217855017370992556781307064909684147168437134776989924009199679451751049463902071325078734830913298092919300478922039915049981436775069764631294555244427773656775976033874151651825477172977355365272140816744612776555341087399480285411816039582955340392622428186544329059791044752703188305422093450163231755612499214835127941203374299609377082285319815967876786649484439753101069672031397428599020725117506952109586811753877365473738437413681941890377760268424324761755950394943183758788668028735377092034491552870881119825181837185102966184009018702288882707564563624506934179688750974857511926101243807641478411329085587568621774527068273061264554966411686308946662247874324443665343317848182648308304843633193092457741108759147340711898447111036284688705080156462824851498096167926419387503557144433132173872921643288661711642424635616025882744218557887417867742743992728956232370743270863365269964744396529799909598704688830879351030911576562139051897511811484501732800720667232930892644887562370383148762106565160784833951237648683236579058733540618052279778526209346470774201891355761827335080115967946200866941125298286735105024851361114064339273375615660053906677176443487974258969905353990822101427209719986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139178
 Posted by Jer on 2005-04-27 17:37:48

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