```Date: Jan 13, 2003 1:06 AM
Author: William Hart
Subject: Re: Brainteaser n

Don't know exactly, but I'm guessing something like1*11*111*....*(10^121-1)/3Bill.Bourbaki wrote:> Here is a test of your powers of inspection and inductive logic. To solve> it requires no more than high school math. It is much easier than it looks.>> X, an integer with just over 6100 decimal digits, is resolved into prime> factors as follows:> 3^54 * 7^20 * 11^60 * 13^19 * 17^6 * 19^6 * 23^5 * 29^3 * 31^7 * 37^38 *> 41^22 * 43^5 * 47^2 * 53^8 * 59 * 61 * 67^3 * 71^3 * 73^13 * 79^8 * 83^2 *> 89^2 * 97 * 101^27 * 103^3 * 107^2 * 109 * 127^2 * 137^13 * 139^2 * 151 *> 157 * 163 * 173^2 * 191 * 197 * 199 * 211^3 * 239^15 * 241^3 * 251^2 *> 271^22 * 277 * 281^3 * 317 * 331 * 353^3 * 397 * 449^3 * 521^2 * 547 *> 613^2 * 617 * 641^3 * 643 * 733 * 757^4 * 859^4 * 1031 * 1231^2 * 1289 *> 1321^2 * 1409^3 * 1933^5 * 2161^3 * 2531^2 * 2689^2 * 2791^3 * 3169 *> 3191^3 * 3541^5 * 4003 * 4013^3 * 4093^5 * 4201 * 4637 * 4649^15 * 5051^2 *> 5171 * 5237 * 6163 * 6299 * 6397 * 7253 * 7841 * 8779^5 * 9091^11 * 9397 *> 9901^9 * 10271 * 10837 * 14197 * 16763^3 * 17837 * 19841 * 21319 * 21401^4> * 21649^10 * 23311 * 25601^4 * 27961^5 * 29611 * 34849 * 42043 * 43037^3 *> 45613 * 52579^6 * 59281 * 60101 * 62003^3 * 62921^2 * 63841 * 69857^3 *> 72559 * 98641 * 123551^3 * 153469 * 206209 * 210631^2 * 216451 * 226549 *> 238681^2 * 307627 * 329401 * 333667^12 * 459691^2 * 493121 * 497867 *> 513239^10 * 538987^2 * 909091^7 * 974293 * 976193 * 999809 * 1192679 *> 1527791^2 * 1580801 * 1659431^2 * 1676321^2 * 2028119^3 * 2071723^6 *> 2462401 * 2906161^7 * 3762091 * 4147571 * 4188901 * 4262077 * 5070721 *> 5882353^6 * 6187457 * 6943319^3 * 7019801 * 7034077 * 9885089 * 10749631 *> 10838689^5 * 12004721 * 28559389 * 29920507 * 35121409^2 * 39526741 *> 45121231 * 52986961^2 * 57009401 * 70541929^2 * 83251631^2 * 99990001^4 *> 103733951 * 121499449^3 * 215257037 * 247629013^3 * 262533041 * 265371653^8> * 505885997^2 * 599144041 * 1052788969^2 * 1056689261^2 * 1058313049^4 *> 1360682471 * 1491383821 * 2182600451 * 2386760191 * 5363222357^6 *> 5964848081^2 * 12171337159 * 14175966169^2 * 20163494891 * 21993833369^3 *> 30703738801 * 43442141653 * 66554101249 * 77843839397^3 * 104984505733 *> 162503518711 * 182521213001^4 * 183411838171 * 291078844423 * 388847808493> * 625437743071 * 985695684401 * 999999000001^3 * 2559647034361 *> 3367147378267 * 8119594779271 * 14103673319201 * 18371524594609 *> 75118313082913 * 78875943472201^2 * 106007173861643 * 203864078068831 *> 422650073734453 * 440334654777631^4 * 549797184491917^2 * 676421558270641 *> 834427406578561 * 1680588011350901 * 1921436048294281 * 1963506722254397^2> * 2324557465671829 * 3199044596370769 * 4855067598095567 *> 9999999900000001^2 * 13168164561429877^2 * 30557051518647307 *> 102598800232111471^3 * 265212793249617641 * 296557347313446299 *> 316877365766624209 * 511399538427507881 * 646826950155548399 *> 722817036322379041 * 909090909090909091^2 * 1111111111111111111^5 *> 1325815267337711173^2 * 1344628210313298373^3 * 1369778187490592461 *> 1855193842151350117 * 2140992015395526641^2 * 2670502781396266997 *> 4185502830133110721^2 * 4458192223320340849 * 7061709990156159479 *> 49172195536083790769 * 57336415063790604359^3 * 79863595778924342083 *> 127522001020150503761 * 377526955309799110357 * 712767480971213008079 *> 1900381976777332243781^2 * 2212394296770203368013^3 *> 3404193829806058997303 * 5295275348767234696493 * 11111111111111111111111^4> * 318727841165674579776721 * 900900900900990990990991^2 *> 1300635692678058358830121^2 * 3931123022305129377976519 *> 5078554966026315671444089 * 7306116556571817748755241 *> 8845981170865629119271997 * 19721061166646717498359681 *> 47198858799491425660200071^2 * 57802050308786191965409441 *> 110742186470530054291318013 * 130654897808007778425046117 *> 154083204930662557781201849 * 297262705009139006771611927 *> 1289981231950849543985493631 * 1595352086329224644348978893 *> 4181003300071669867932658901 * 4531530181816613234555190841 *> 9512538508624154373682136329 * 59779577156334533866654838281 *> 90077814396055017938257237117 * 201763709900322803748657942361^2 *> 241573142393627673576957439049 * 909090909090909090909090909091 *> 129063282232848961951985354966759 * 965194617121640791456070347951751 *> 1976730144598190963568023014679333^2 * 15763985553739191709164170940063151> * 846035731396919233767211537899097169 *> 5538396997364024056286510640780600481 *> 10288079467222538791302311556310051849 *> 16205834846012967584927082656402106953 *> 316362908763458525001406154038726382279^2 *> 403513310222809053284932818475878953159 *> 5076141624365532994918781726395939035533 *> 18998088572819375252842078421374368604969 *> 28213380943176667001263153660999177245677 *> 45994811347886846310221728895223034301839 *> 346895716385857804544741137394505425384477 *> 632527440202150745090622412245443923049201 *> 3660574762725521461527140564875080461079917 *> 4222100119405530170179331190291488789678081 *> 49207341634646326934001739482502131487446637 *> 136614668576002329371496447555915740910181043 *> 4340876285657460212144534289928559826755746751 *> 310170251658029759045157793237339498342763245483 *> 362853724342990469324766235474268869786311886053883 *> 9090909090909090909090909090909090909090909090909091 *> 109399846855370537540339266842070119107662296580348039 *> 246829743984355435962408390910378218537282105150086881669547 *> 900900900900900900900900900900990990990990990990990990990991 *> 153211620887015423991278431667808361439217294295901387715486473457925534859> 044796980526236853>> Provide a short (37 ASCII characters suffice), simple (the only operators> being add and multiply; no factorials) expression that yields X.>> Hints (1) You do not need to numerically compute X. It will not help.>       (2) Sometimes, what is not there is as significant as what is there.>       (3) The expression is elegant in its economy.>> Have fun!>> --> Bourbaki
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