What is the answer 2007^2007^2007^2007?
I only need the last 3 digits. I know the last 2 numbers have to either be 01, 07, 49, or 43.
How would I find this number?
2007-11-02 09:31:58 · 10 answers · asked by neo p 2 in Science & Mathematics ➔ Mathematics
401
2007-11-02 09:35:22 · answer #1 · answered by BaracktheVote 2 · 0⤊ 2⤋
All that really matters is the last couple digits in 2007
07^0 --> 01
07^1 --> 07
07^2 --> 49
07^3 --> 43
07^4 --> 01
07^5 --> 07
07^6 --> 49
07^7 --> 43
The pattern repeats every 4. If you take the number, divide it by 4 and take the remainder, you'll know which number comes out.
2007^2007 --> 43
Now try this again with 43:
43^0 --> 01
43^1 --> 43
43^2 --> 49
43^3 --> 07
43^4 --> 01
43^5 --> 43
43^6 --> 49
43^7 --> 07
Same thing, just reordered. So again we have a remainder of 3.
2007^2007^2007 --> 07
Finally:
49^0 --> 01
49^1 --> 07
49^2 --> 49
49^3 --> 43
It's back to the original pattern, so it must end with 43
2007^2007^2007^2007 --> 43
Oops... just noticed you wanted the last *three* digits. I like the answer below, though I don't understand it fully.
2007-11-02 16:54:25 · answer #2 · answered by Puzzling 7 · 1⤊ 0⤋
Last 3 digits are 343
2007^2007^2007^2007 = 7^ 2007^2007^2007 (mod 1000)
Ï(1000) = 400
2007^2007^2007 = 7^2007^2007(mod 400)
Ï(400) = 160
2007^2007 = 87^2007 = ... = 103 (mod 160)
7^103 = 7^3 = 343 (mod 400)
7^343 = 7 * 49 ^ 171 = .... = 343 (mod 1000)
2007-11-02 16:56:30 · answer #3 · answered by Ivan D 5 · 2⤊ 0⤋
The answer is 16225178746401.
Therefore the last two digits are 01.
You find this by just entering this into a calculator:
2007 * 2007 * 2007 * 2007.
Where "*" is times. (or multiply.)
2007-11-02 16:36:04 · answer #4 · answered by Anonymous · 0⤊ 3⤋
807
2007-11-02 16:44:36 · answer #5 · answered by Niya M 1 · 0⤊ 1⤋
The answer is a whole bunch!
but seriously just multiply 7*7*7*7 and you will have your answer the two zeros in front mean you don't have to worry about them since you only want lasty 3 numbers
2007-11-02 16:34:51 · answer #6 · answered by Anonymous · 0⤊ 4⤋
16225178746401
i think
2007-11-02 16:47:08 · answer #7 · answered by melstxi055 3 · 0⤊ 2⤋
overflow error...lol
2007-11-02 16:57:23 · answer #8 · answered by John P 2 · 0⤊ 3⤋
undefined
2007-11-02 16:38:03 · answer #9 · answered by Anonymous · 0⤊ 3⤋
A very big number.
2007^2007 =
16314605714687673100219161988221
59051829221089874043784187650689
27503230603942394036965618267162
69183744286650077283106417262070
38681918231367024041678219029799
21698186677089033622516321277953
10242141538052881817063065329725
41418657042472116588038422083621
97277303427121903754703807849329
88542284134124507653358027528106
79631982070064711707569949048263
60657191473471275712342626409252
81200048765495245746258125202397
47186250057525320395798655995302
91792214971852417878942451095150
62842521950258480107071006933067
54335210537773553923807001377973
58190841023173651478340362529204
45597852373469464933358743704855
18808434498786097277847304253983
06262209009100302431330777480966
36794353164578522888857881837043
21212603620156876288242227673033
90248946185980807205983674431470
10318722850998596344284937602588
15156591392043545733404816951476
91243513959269155489000051079398
70885748926502983652482207392398
28923170534565961757683913268494
07390334197894040104134124158904
43721763374422715662742069231036
65888769044749061196406563360090
90556296737743411721018311144535
21702586164711667890001015971356
60276401463142043929976624709724
32879282995742204308753717879575
86477218546176739385924199923209
20917539991610303182692147549245
71963159355206248122516949558768
45371629366273520636698693605424
70442040463175277434551058391143
65020892835847550233917496742026
96799026646581142344132536466689
90428604242697559857567177309990
47598611204004019487050374925139
89337593522479668752257755675941
90209918523755414374865176084285
43269856231288891826367085951725
67410962602190518046611666197715
67825636407678105277470556285310
62056538632420611318856864435605
98573568085436649055893711511908
75478671191725973512380505893222
68750902004874511200777176495530
75575503220019193795364522691566
37570639676868959884035264182305
39376546037003876670242151992373
96744785896532371190719225599092
10293596043287664220699686719190
81979032540651846677211856682947
81547580783618298053398421405368
77388530591895758845746157553058
66464237994838787908227762252835
49789414467760475990305056214887
67501000876280612286575512127556
47596779049507838932073510212179
35470775265956805544003684592264
50944178849240467865779814317007
96876505317193541397691960050013
42315458830644644251127472322836
60739974075836826864673520408037
91019506735395126455177520839156
27087436663427797490047240479251
57702126529475456581827940549061
21983354277172666791641130825385
60381682672879310769431847091067
68836609569020865957914794570252
28534735526355341403823093037779
50425443446724647072840398854653
20015844579846408011500806127198
94295345647928742912612458187025
14956613295757826200587896655617
16719470124221795875969262244841
32219092653628493411015388967193
74297181506945626681830899361082
17588258048154216467741811634089
43162720490820090671235223645285
11646087005155543082600495645674
71459009228328887405507016042919
30516794538042710882409957144952
87536761378107585304471702025690
38123743569962867717292953981124
66906501168350289075899108008520
51576339702128919877730936870117
98574109235019698651104787736539
03699197912297908533711497227232
92678177205635678230292598408904
56926656652909696594068719800187
41066790089375338891716112009070
91212256713279948375563588661379
53648953584541796829449368195994
09259644069296990066176672218326
10569446092009445906651399279429
32607074402971949610315730694029
33820865260574953275552269012269
91958507823554106085474705558869
45614660288497635650128282415038
87371454415825187174123047124428
96555918635065661067953888197801
88833094428377889515111801493863
21628256574854222687337914749700
94878509775285438890316897994847
55702907033188341688570861620268
84996378694574719417715017198218
67186477996944237308394784224584
93685477488008379845958058718144
18619620250430016966689420999836
93615311522514026707878870470710
49415711093008135194582239773277
57730018467737893821357739016393
73798151706392916494862927898986
34906646220424941180088128828829
19705833036271286195708724081415
16094456838371121370175955073467
94006856000647005501898922929846
15393921879628234593579234420657
37766478005527385267444939667056
17379100573317705340545281115457
24807738396593703463769099555899
54534463995402397547550905549017
41064115038670213867607618630149
35241290311824525268727528109561
67849843667679892379716531335973
29118214006238594099241520690630
02606388280411771677028471887123
06493492372142866618404908913176
54030952366549559176082480786655
05938880952050718263761568324771
49880519149263313202959954492148
66619702999475887866781898710889
66477407525129965638506232281095
36022666509972476172556459154412
19375552485928452331588277656632
22042401666411324880949881337096
25618201627915826412144882338368
99677241035926715177068155687444
26523608840138911714539589445182
34290650299585576981492919941107
10260947893394646261930248865632
36872662273290693765905066092598
64305413378209143196536682218734
96515400783644691617385504947828
57953599406614823850511779698786
91838865273359122035277482634624
99102167592462431225436029388484
29176583830774725378097405954813
23814151252029906869583239205987
30920623832520417050545422826928
95103797418414876506955754092950
59317151152603651256685226830058
55508399819407071084730775708819
78961720357534435732502475238487
52690656937029948286384387684965
34182574105672247872168890732731
20095695064749134557169837596440
81778727720259029665694948573652
67255713677133561547969896429522
82243118652905333146492789296637
85628791059773039220218420361711
03420525191259589291180958162828
53849025184090592088836475653212
59466389159493001180027830181032
01677127173934202638381916350590
93409866889426369493410344428996
07560777487439592104091976472130
06839217933959866202483201890809
51927880128889774489640070710220
96271976415983960600086952689645
54981226251385200347359377102338
42029608413372668220552448943181
15626747268831051684933685907960
32830924999538553468389382057082
60700710168088786517941756230281
76614181228360077882678513082102
12677957457252545213860172852629
88853513052963250671784761373493
70135741313308883039679816779268
89819182812687810885966489071842
74633724520274913262414935417093
91651625930389901245701251560820
23268444123374964789450321183919
23014778607915469408747170495370
71793531373218290246791145310292
22105937289264816915738818462542
77373279055909079301715014253588
84742304929646018753182091973651
54939042362137576756081363036809
89586717189185046309782767730617
25084597786832034498958720078262
84435526596201784247913262269519
02374157961233078917157266273709
91180441369098736393737440065785
95380707369323173218823399525819
50548422144343493289702293960474
93455994166543113414231137214737
09326274240710315108579865846837
89830262663716323838605811095635
09543
2007-11-02 16:37:39 · answer #10 · answered by Anonymous · 0⤊ 4⤋