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Factorials AND Powers (Posted on 2013-07-11) Difficulty: 3 of 5
Recall that if n is a positive integer, then n! is the product of all the integers from 1 to n, inclusive. Show that. (210)! > 2 2^13 .

No Solution Yet Submitted by Danish Ahmed Khan    
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re: solution (exact confirmation) Comment 2 of 2 |
(In reply to solution by Charlie)

using Mathematica I am able to calculate both values exactly and get the difference of (2^10)! - 2^(2^13) as being the positive integer:
5418528796058857283076921944683854738001553963538013444482870270683210\
6120733766037331409841362145867190791884570898075393199416577018736826\
0454133333721939108367528012764992679020156897521961702771435925880885\
4990503564086539852407233389989730034020943820582577289055681464892485\
0445227610359697856535147750617390741068786717747872949663331652907231\
5196337578015720275613970573256601090358375148304886802129854130812002\
2868637289995682463781159398643003313465734430290172315631615403045512\
1073521004226992301132500375102554693604840871461232403636220620760021\
0555305637613229186269067321295489124274714522651296057249355704008686\
9608793106655849281785136162753701159398032435239242390298556581621313\
4534481260813001439472682194489609382719688093171927446083589268982132\
6725964937436275553878930499592450149578664947053062306646756454600991\
3412197460461986369275263546587142387210505167630819147631393310983660\
0951021321433328006840345923636110803430451697393157227760864381866007\
6599643424027508648364336968793882051526138019081956268678513487821848\
4280890066230094392653561523674358608539137194531110039357332638541414\
9189795503075084067923985533046814790177288451794497439540636065611035\
6570765901993192504866047527250365287505895702659460390141762178270944\
7744192876126718221732196724442860866332331372725095750443439294847464\
9001121711004408567279455223654575004808900139924629879422975661433086\
6594859834529688785712254793201232638598851657896978247669187065692573\
8750601483513153143723008792597492122266544168315811299303281516709334\
9515276502673377915442196476123854740080753657322426656398228711931001\
6467045169811954977907480999813485192554464446168043980675054000873710\
9849556309439284965943955943416044441726931766076489833933367236035421\
1248625366605987239137291672057183790959961893651197705661390885205778\
2043120223045049510727729579544474217228594066023310725912828250066748\
4414467153463716549569690342191528711000826897029755698387859441600844\
8676361112853563986388901710078418459513449908889362054729881446958122\
8457696109105215242442081783339303001585773979454191043188495056170745\
5512562091903903310281349879620250260391646983140776935972169594637922\
9975590865801328849711689700964521614539328036658095649668006770843091\
3312365763282216490433708348239750771619777245149069775795458721933473\
0313424038159818722090996224578387650494452913097560243328790195635808\
0415645980138425261314490310391081081955866044147517713245888678736120\
6324432349659637029968069976602171534681452761755767971984810310339581\
1770239991845623893477457298364043491245661488528767857727333945964182\
18530909193423531049412338002813494334524284207104

  Posted by Daniel on 2013-07-11 21:34:09

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