Can Modern Calculators Solve (8^2003 + 6^2003) / 49?

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Discussion Overview

The discussion revolves around the mathematical expression (8^2003 + 6^2003) / 49 and whether modern calculators can solve it. Participants explore the computation of the expression, its approximate value, and the reasoning behind the calculations, with a focus on both theoretical and practical aspects of large number computations.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that calculators may struggle with the expression due to its complexity.
  • Another participant provides a logarithmic approach to estimate 8^2003 and 6^2003, concluding that the second term can be neglected in comparison to the first, leading to an approximate value of 1.5816 * 10^1807.
  • A different participant claims to have obtained a precise value for the expression using Mathematica, presenting a lengthy numerical result and an approximate value of 1.5814223227342232267895223637314066 * 10^1807.
  • Another participant states the exact answer, including a correction to their previous post, and provides a detailed breakdown of the components of the expression.
  • Several participants express curiosity about the reasoning behind the calculations and the nature of the question itself, with some humorously questioning the need for such a computation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity or significance of solving the expression, with some focusing on the computational aspects and others questioning the purpose of the inquiry.

Contextual Notes

Participants express uncertainty about the computational capabilities of calculators for such large numbers and the relevance of the results. There are also indications of misinterpretations and corrections made during the discussion.

scilover89
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Even calculator can't solve this...

(8^2003+6^2003)/49=?

Who can solve this?
 
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[tex]8^{2003} = 10^{2003*log_{10}8} = 10^{1808.88924} = 7.75 * 10^{1808}[/tex]

[tex]6^{2003} = 10^{2003*log_{10}6} = 10^{1558.63695} = 4.335 * 10^{1558}[/tex]

The second can be neglected in comparison to the first giving

[tex](8^{2003}+6^{2003})/49 = (about)~ 1.5816 * 10^{1807}[/tex]

Also, if you wrote out the full number (in decimal expansion) in all its gory detail, the digits after the decimal point would be .04081632653... for whatever that's worth.
 
Last edited:
Well, I didn't do the arithmetic, but the answer is

110699562591395625875266564924664097310974709512929097789175911617601046454386434533363625521484979625995866415556215005295416133194216915274253564533823808741077943952672510750053902252973351456954446065237629947590350789140326338000369452446840290082144467142045178897824353048670587312080224265459784206322855624222209627723142215253195344567886035909787077726154777006320959340849530325395879878645900740268181333554850414711304850535157904078675787256343935250506945484632580361260539052711292135393964305721326164034185323257036401562064939229517300512382832378049844366899876452596800955806420515203883818227428415114965787363900634482730394595855901269536477229409114070793987701830131336961091311521917948013656268286590558122942173068042452683584041597393131362115133639708695813827166004500777279577036282790847755599032408449092996078742277433061567299573578686181516485959696804800782360503486653196727233559342142902572693633989299389429306974042715177724597042437294815094190562672889102497380940799682008786172658233122667320788812823727542218978920706958595020667644482284910188722257885885010942161301492075556745333658141372608295823959953020682907150950904979738403629013487885794876482903052545000231653116968614767872331012877153046697429893686056710998765089687784315909815005258973458134465324287048736599893117632184261219444205283823063443143881361385024937369090408673392508695811724593424721886293429928788520837043197212862355297138917320309016807737396766789530004574754173260914474719164345351785481277844433138044222960404781867964113414476335964916396492692453035888217537736329111435482807135250055792650863889863243772287640514370785654038798197610745561837609318531738132668887103225077809387770418238590052166821081931085756853573798577748014227700555866270649651879215104

divided by 7, which can be shortened to approximately

1.5814223227342232267895223637314066 * 10^1807

Mathematica did it, not me :redface: Excuse the strange spacing too...it's late and I feel no urge to write simple latex.
 
Last edited:
The exact answer is:

15814223227342232267895223560666299615853529930418442541310844516800149493483776361909089360212139946570838059365173572185059447599173845039179080647689115534439706278953215821436271750424764493850635152176804278227192969877189476857195636063834327154592066734577882699689193292667226758868603466494254886617550803460315661103306030750456477795412290844255296818022111000902994191549932903627982839806557248609740190507835773530186407219308272011239398179477705035786706497804654337322934150387327447913423472245903737719169331893862343080294991318502471501768976054007120623842839493228114422258060073600554831175346916444995112480557233497532913513693700181362353889915587724399141100261447333851584473074559706859093752612370079731848881866863207526226291656770447337445019091386956544832452286357253897082433754684406822228433201207013285154106039633294509614224796955168788069422813829257254622929069521885246747651334591843224670519141328484204186710577530739674942434633899259299170080381841300356768705828526001255167522604731809617255544689103934602711274386708370717238234926040701455531751126555001563165900213153650963619094020196086899403422850431526129592992986425676914804144783983684982354700436077857175950445281230681124618716125307578099632841955150958714109298526826330844259286465567636876352189183864105228556159661740608745634886469117580491877697337340717848195584344096198929813687389227632103126613347132684074405291885316123193613876988188615573829676770966684218572082107739037273496388452049335969354468263490448292031851486397409709159059210905137845199498956064719412602505390904158776497543876464293684664409127123320538898234359195826522005542599658677937405372759790248304666983871889296829912538631176941436023831583133012250979081971225392573461100079409467235664554173586 + 2/7

As 82003+62003 is:

774896938139769381126865954472648681176822966590503684524231381323207325180705041733545378650394857381971064908893505037067912932359518406919774951736766661187545607668707575250377315770813460198681122456663409633132455523982284366002586167127882030575011269994316252284770471340694111184561569858218489444259989369555467394061995506772367411975202251368509544083083439044246715385946712277771159150521305181877269334883952902979133953746105328550730510794407546753548618392428062528823773368979044947757750140049283148239297262799254810934454574606621103586679826646348910568299135168177606690644943606427186727591998905804760511547304441379112762170991308886755340605863798495557913912810919358727639180653425636095593878006133906860595211476297168785088291181751919534805935477960870696790162031505440957039253979535934289193226859143650972551195942031430971097015050803270615401717877633605476523524406572377090634915395000318008855437925095726005148818299006244072179297061063705659333938710223717481666585597774061503208607631858671245521689766092795532852444948710165144673511375994371321055805201195076595129110444528897217335606989608258070767719671144780350056656334858168825403094415200564135380321367815001621571818780303375106317090140071326882009255802396976991355627814490211368705036812814206941257270009341156199251823425289828536109436986761444102007169529695174561583632860713747560870682072153973053204054009501519645859302380490036487079972421242163117654161777367526710032023279212826401323034150417462498368944911031966309560722833473075748793901334351754414775448847171251217522764154303780048379649946750390548556047229042706406013483600595499578271587383275218932863265229722166928682209722575544665714392927670130365167747573517600297975016590044236099593903891063894547563154505728

Edit my fault[/size] I misread the post, I've corrected it now
 
Last edited:
The question is...

Why?
 
FZ+ said:
The question is...

Why?
The answer is,...

Why not?
 
Yes, that is the question.

EDIT : DAMN, beat to the punch...and by a dissenter, at that. bah !
 

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