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 Number power (Posted on 2006-12-30)
Determine the last two and the first two digits of:

32^1+32^2+32^3+...+32^2007

 No Solution Yet Submitted by atheron Rating: 3.0000 (1 votes)

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 All the digits. | Comment 3 of 4 |

Although the precision of UBASIC is not sufficient to calculate directly all 3021 digits of the given sum,  it is sufficient to calculate the last 2500 digits and also the first 1500 digits separately. You can combine them, throwing away the overlap (but verifying the overlaps match), to get all the digits.

The number begins      707611321018523482405446470261455238693602066936634350455852177
30210667246687593047166831585039311342054810839657229652327337251808816804064427
47110497328567396058247199702474173979301744682499801842747395600326233270815970
00866383027743724684969441439019883247052213375377952497914672633074955713630385
42845854971841139681466726115429624429551449328071684167188997104214390003654190
67670413756986068005618643140097099199768410290415228975048582855660831013882544
11436909410819559053790997217475073039810984148952097354205444597880401871600775
62785456402292437561437493000207688555757021359280240137535609412220702996706385
52228505688140707318964457694633291274799066396536712673355102787426828070915824
23762300964716597257263006685057034432501528020333554592876263922989013907812399
95086557357461262563905188409564796434208718661631682772139462977278435343794775
78016104348991083723638614924091084902110219469814198713276014978217810197088646

and ends

5444597880401871600775627854564022924375614374930002076885557570213592802401375
35609412220702996706385522285056881407073189644576946332912747990663965367126733
55102787426828070915824237623009647165972572630066850570344325015280203335545928
76263922989013907812399950865573574612625639051884095647964342087186616316827721
39462977278435343794775780161043489910837236386149240910849021102194698141987132
76014978217810197088646547228120783332279557142596558517248179428526977317032816
25304100376022871969741880413392869187150552450343896658540219107342968400510154
47027998237937504524999971785456196670920528944010748418858754769348326415061409
69108991583756733785171213054018812097296296735748511749829291901510695064235226
42878969701091829403951859043062057731838874582347657141350622994778806810861934
36810885899840510041374130711423676128623577199974392868797564490139952575611782
69908413925287099343331645098386614499202706031437500703016714373800250320487812
52613350323141562145276162717704094689403176702145707813099483825228902438015268
44516571840811331514820065677040223722249664385818873251619881791446493527984501
62029745942643337267280355804113720184410787025623466421159911689866419930872158
86360964445065391905847307674191260038557680936219360705830453323579390419049111
36987748184126999672511309348861253150937430911604207382415499315430358885076707
34716848919486893487652425554057653553899476304486834248585352027463476144580381
46978160502643028197175453415424381210891550719859216078198259929311097328015272
76652812144498473977578509056037858739921268843972533578275606842070278291946035
84143818097182638473299754355139338743219363630686155250466874244374907530491717
14629461242504384926387818294979354461857474050355958672420239535424362848150727
50366983009582342561630794279776580279221410905410339679590002356926373558272647
36329942727794082253474711764215218371689106184737858390837906376694504437482644
14966121911610645978997060609427223188102017339524913396418051516489189915683509
99986524610042272317192437040366372257432953645543622402705039566707386937317379
65265816432146942688798278440767562966314025689307271765586976816963326701387582
81974630212538682395547993749059245578945685147281840854241010836134351522306975
13065603658693216679172251227614915942847285290179078438425577923908770627942343
33375789587485454618649822971647121320462949972270120644511994749298018146013743
13630113848132831645187234255569712351039395554495637585109796061392556801838231
430927935480869717024

so, taking the beginning up to where it has 544459788... the whole number is

707611321018523482405446470261455238693602066936634350455852177
30210667246687593047166831585039311342054810839657229652327337251808816804064427
47110497328567396058247199702474173979301744682499801842747395600326233270815970
00866383027743724684969441439019883247052213375377952497914672633074955713630385
42845854971841139681466726115429624429551449328071684167188997104214390003654190
67670413756986068005618643140097099199768410290415228975048582855660831013882544
1143690941081955905379099721747507303981098414895209735420
5444597880401871600775627854564022924375614374930002076885557570213592802401375
35609412220702996706385522285056881407073189644576946332912747990663965367126733
55102787426828070915824237623009647165972572630066850570344325015280203335545928
76263922989013907812399950865573574612625639051884095647964342087186616316827721
39462977278435343794775780161043489910837236386149240910849021102194698141987132
76014978217810197088646547228120783332279557142596558517248179428526977317032816
25304100376022871969741880413392869187150552450343896658540219107342968400510154
47027998237937504524999971785456196670920528944010748418858754769348326415061409
69108991583756733785171213054018812097296296735748511749829291901510695064235226
42878969701091829403951859043062057731838874582347657141350622994778806810861934
36810885899840510041374130711423676128623577199974392868797564490139952575611782
69908413925287099343331645098386614499202706031437500703016714373800250320487812
52613350323141562145276162717704094689403176702145707813099483825228902438015268
44516571840811331514820065677040223722249664385818873251619881791446493527984501
62029745942643337267280355804113720184410787025623466421159911689866419930872158
86360964445065391905847307674191260038557680936219360705830453323579390419049111
36987748184126999672511309348861253150937430911604207382415499315430358885076707
34716848919486893487652425554057653553899476304486834248585352027463476144580381
46978160502643028197175453415424381210891550719859216078198259929311097328015272
76652812144498473977578509056037858739921268843972533578275606842070278291946035
84143818097182638473299754355139338743219363630686155250466874244374907530491717
14629461242504384926387818294979354461857474050355958672420239535424362848150727
50366983009582342561630794279776580279221410905410339679590002356926373558272647
36329942727794082253474711764215218371689106184737858390837906376694504437482644
14966121911610645978997060609427223188102017339524913396418051516489189915683509
99986524610042272317192437040366372257432953645543622402705039566707386937317379
65265816432146942688798278440767562966314025689307271765586976816963326701387582
81974630212538682395547993749059245578945685147281840854241010836134351522306975
13065603658693216679172251227614915942847285290179078438425577923908770627942343
33375789587485454618649822971647121320462949972270120644511994749298018146013743
13630113848132831645187234255569712351039395554495637585109796061392556801838231
430927935480869717024

(just consider the digits; ignore the unevenness of the line lengts, coming about due to where the digits appear in the cutting and pasting.)

 Posted by Charlie on 2006-12-30 16:31:31

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