Для перевода 55-ого числа 6757685785675876857685769798647967548675487695476985476576567958754647564859643756437658746587436587436587436584356847564833564385684356438564568436584568743566666375684356437564835687456874567436587465438654 в десятичное необходимо записать его в виде многочлена, состоящего из произведений цифр вида:
A55 = an-1 ∙ 55n-1 + an-2 ∙ 55n-2 + ∙∙∙ + a0 ∙ 550
В результате преобразований получим:
675768578567587685768576979864796754867548769547698547657656795875464756485964375643765874658743658743658743658435684756483356438568435643856456843658456874356666637568435643756483568745687456743658746543865455=6 ∙ 55207 + 7 ∙ 55206 + 5 ∙ 55205 + 7 ∙ 55204 + 6 ∙ 55203 + 8 ∙ 55202 + 5 ∙ 55201 + 7 ∙ 55200 + 8 ∙ 55199 + 5 ∙ 55198 + 6 ∙ 55197 + 7 ∙ 55196 + 5 ∙ 55195 + 8 ∙ 55194 + 7 ∙ 55193 + 6 ∙ 55192 + 8 ∙ 55191 + 5 ∙ 55190 + 7 ∙ 55189 + 6 ∙ 55188 + 8 ∙ 55187 + 5 ∙ 55186 + 7 ∙ 55185 + 6 ∙ 55184 + 9 ∙ 55183 + 7 ∙ 55182 + 9 ∙ 55181 + 8 ∙ 55180 + 6 ∙ 55179 + 4 ∙ 55178 + 7 ∙ 55177 + 9 ∙ 55176 + 6 ∙ 55175 + 7 ∙ 55174 + 5 ∙ 55173 + 4 ∙ 55172 + 8 ∙ 55171 + 6 ∙ 55170 + 7 ∙ 55169 + 5 ∙ 55168 + 4 ∙ 55167 + 8 ∙ 55166 + 7 ∙ 55165 + 6 ∙ 55164 + 9 ∙ 55163 + 5 ∙ 55162 + 4 ∙ 55161 + 7 ∙ 55160 + 6 ∙ 55159 + 9 ∙ 55158 + 8 ∙ 55157 + 5 ∙ 55156 + 4 ∙ 55155 + 7 ∙ 55154 + 6 ∙ 55153 + 5 ∙ 55152 + 7 ∙ 55151 + 6 ∙ 55150 + 5 ∙ 55149 + 6 ∙ 55148 + 7 ∙ 55147 + 9 ∙ 55146 + 5 ∙ 55145 + 8 ∙ 55144 + 7 ∙ 55143 + 5 ∙ 55142 + 4 ∙ 55141 + 6 ∙ 55140 + 4 ∙ 55139 + 7 ∙ 55138 + 5 ∙ 55137 + 6 ∙ 55136 + 4 ∙ 55135 + 8 ∙ 55134 + 5 ∙ 55133 + 9 ∙ 55132 + 6 ∙ 55131 + 4 ∙ 55130 + 3 ∙ 55129 + 7 ∙ 55128 + 5 ∙ 55127 + 6 ∙ 55126 + 4 ∙ 55125 + 3 ∙ 55124 + 7 ∙ 55123 + 6 ∙ 55122 + 5 ∙ 55121 + 8 ∙ 55120 + 7 ∙ 55119 + 4 ∙ 55118 + 6 ∙ 55117 + 5 ∙ 55116 + 8 ∙ 55115 + 7 ∙ 55114 + 4 ∙ 55113 + 3 ∙ 55112 + 6 ∙ 55111 + 5 ∙ 55110 + 8 ∙ 55109 + 7 ∙ 55108 + 4 ∙ 55107 + 3 ∙ 55106 + 6 ∙ 55105 + 5 ∙ 55104 + 8 ∙ 55103 + 7 ∙ 55102 + 4 ∙ 55101 + 3 ∙ 55100 + 6 ∙ 5599 + 5 ∙ 5598 + 8 ∙ 5597 + 4 ∙ 5596 + 3 ∙ 5595 + 5 ∙ 5594 + 6 ∙ 5593 + 8 ∙ 5592 + 4 ∙ 5591 + 7 ∙ 5590 + 5 ∙ 5589 + 6 ∙ 5588 + 4 ∙ 5587 + 8 ∙ 5586 + 3 ∙ 5585 + 3 ∙ 5584 + 5 ∙ 5583 + 6 ∙ 5582 + 4 ∙ 5581 + 3 ∙ 5580 + 8 ∙ 5579 + 5 ∙ 5578 + 6 ∙ 5577 + 8 ∙ 5576 + 4 ∙ 5575 + 3 ∙ 5574 + 5 ∙ 5573 + 6 ∙ 5572 + 4 ∙ 5571 + 3 ∙ 5570 + 8 ∙ 5569 + 5 ∙ 5568 + 6 ∙ 5567 + 4 ∙ 5566 + 5 ∙ 5565 + 6 ∙ 5564 + 8 ∙ 5563 + 4 ∙ 5562 + 3 ∙ 5561 + 6 ∙ 5560 + 5 ∙ 5559 + 8 ∙ 5558 + 4 ∙ 5557 + 5 ∙ 5556 + 6 ∙ 5555 + 8 ∙ 5554 + 7 ∙ 5553 + 4 ∙ 5552 + 3 ∙ 5551 + 5 ∙ 5550 + 6 ∙ 5549 + 6 ∙ 5548 + 6 ∙ 5547 + 6 ∙ 5546 + 6 ∙ 5545 + 3 ∙ 5544 + 7 ∙ 5543 + 5 ∙ 5542 + 6 ∙ 5541 + 8 ∙ 5540 + 4 ∙ 5539 + 3 ∙ 5538 + 5 ∙ 5537 + 6 ∙ 5536 + 4 ∙ 5535 + 3 ∙ 5534 + 7 ∙ 5533 + 5 ∙ 5532 + 6 ∙ 5531 + 4 ∙ 5530 + 8 ∙ 5529 + 3 ∙ 5528 + 5 ∙ 5527 + 6 ∙ 5526 + 8 ∙ 5525 + 7 ∙ 5524 + 4 ∙ 5523 + 5 ∙ 5522 + 6 ∙ 5521 + 8 ∙ 5520 + 7 ∙ 5519 + 4 ∙ 5518 + 5 ∙ 5517 + 6 ∙ 5516 + 7 ∙ 5515 + 4 ∙ 5514 + 3 ∙ 5513 + 6 ∙ 5512 + 5 ∙ 5511 + 8 ∙ 5510 + 7 ∙ 559 + 4 ∙ 558 + 6 ∙ 557 + 5 ∙ 556 + 4 ∙ 555 + 3 ∙ 554 + 8 ∙ 553 + 6 ∙ 552 + 5 ∙ 551 + 4 ∙ 550 = 6 ∙ INF + 7 ∙ INF + 5 ∙ INF + 7 ∙ INF + 6 ∙ INF + 8 ∙ INF + 5 ∙ INF + 7 ∙ INF + 8 ∙ INF + 5 ∙ INF + 6 ∙ INF + 7 ∙ INF + 5 ∙ INF + 8 ∙ INF + 7 ∙ INF + 6 ∙ INF + 8 ∙ INF + 5 ∙ INF + 7 ∙ INF + 6 ∙ INF + 8 ∙ INF + 5 ∙ INF + 7 ∙ INF + 6 ∙ INF + 9 ∙ INF + 7 ∙ INF + 9 ∙ INF + 8 ∙ INF + 6 ∙ INF + 4 ∙ INF + 7 ∙ 1.1071234265923E+308 + 9 ∙ 2.0129516847134E+306 + 6 ∙ 3.6599121540243E+304 + 7 ∙ 6.6543857345896E+302 + 5 ∙ 1.2098883153799E+301 + 4 ∙ 2.1997969370544E+299 + 8 ∙ 3.9996307946444E+297 + 6 ∙ 7.2720559902625E+295 + 7 ∙ 1.3221919982296E+294 + 5 ∙ 2.4039854513265E+292 + 4 ∙ 4.3708826387754E+290 + 8 ∙ 7.947059343228E+288 + 7 ∙ 1.4449198805869E+287 + 6 ∙ 2.6271270556126E+285 + 9 ∙ 4.7765946465683E+283 + 5 ∙ 8.684717539215E+281 + 4 ∙ 1.5790395525846E+280 + 7 ∙ 2.8709810046992E+278 + 6 ∙ 5.2199654630894E+276 + 9 ∙ 9.4908462965262E+274 + 8 ∙ 1.7256084175502E+273 + 5 ∙ 3.1374698500913E+271 + 4 ∙ 5.7044906365297E+269 + 7 ∙ 1.0371801157327E+268 + 6 ∙ 1.8857820286049E+266 + 5 ∙ 3.4286945974634E+264 + 7 ∙ 6.2339901772061E+262 + 6 ∙ 1.133452759492E+261 + 5 ∙ 2.0608231990764E+259 + 6 ∙ 3.746951271048E+257 + 7 ∙ 6.8126386746327E+255 + 9 ∙ 1.238661577206E+254 + 5 ∙ 2.2521119585563E+252 + 8 ∙ 4.0947490155569E+250 + 7 ∙ 7.4449982101034E+248 + 5 ∙ 1.3536360382006E+247 + 4 ∙ 2.461156433092E+245 + 6 ∙ 4.4748298783491E+243 + 4 ∙ 8.1360543242712E+241 + 7 ∙ 1.4792826044129E+240 + 5 ∙ 2.6896047352963E+238 + 6 ∙ 4.8901904278114E+236 + 4 ∙ 8.8912553232934E+234 + 8 ∙ 1.6165918769624E+233 + 5 ∙ 2.9392579581135E+231 + 9 ∙ 5.3441053783882E+229 + 6 ∙ 9.7165552334331E+227 + 4 ∙ 1.7666464060788E+226 + 3 ∙ 3.2120843746886E+224 + 7 ∙ 5.8401534085248E+222 + 5 ∙ 1.0618460742772E+221 + 6 ∙ 1.9306292259586E+219 + 4 ∙ 3.5102349562884E+217 + 3 ∙ 6.3822453750698E+215 + 7 ∙ 1.1604082500127E+214 + 6 ∙ 2.1098331818413E+212 + 5 ∙ 3.8360603306205E+210 + 8 ∙ 6.9746551465827E+208 + 7 ∙ 1.2681191175605E+207 + 4 ∙ 2.3056711228372E+205 + 6 ∙ 4.1921293142495E+203 + 5 ∙ 7.6220532986355E+201 + 8 ∙ 1.3858278724792E+200 + 7 ∙ 2.5196870408712E+198 + 4 ∙ 4.5812491652204E+196 + 3 ∙ 8.3295439367644E+194 + 6 ∙ 1.5144625339572E+193 + 5 ∙ 2.7535682435585E+191 + 8 ∙ 5.0064877155609E+189 + 7 ∙ 9.1027049373834E+187 + 4 ∙ 1.6550372613424E+186 + 3 ∙ 3.0091586569863E+184 + 6 ∙ 5.4711975581568E+182 + 5 ∙ 9.9476319239215E+180 + 8 ∙ 1.8086603498039E+179 + 7 ∙ 3.2884733632798E+177 + 4 ∙ 5.9790424786906E+175 + 3 ∙ 1.0870986324892E+174 + 6 ∙ 1.9765429681622E+172 + 5 ∙ 3.5937144875676E+170 + 8 ∙ 6.534026341032E+168 + 4 ∙ 1.1880047892786E+167 + 3 ∙ 2.1600087077792E+165 + 5 ∙ 3.9272885595985E+163 + 6 ∙ 7.1405246538155E+161 + 8 ∙ 1.2982772097846E+160 + 4 ∙ 2.3605040177902E+158 + 7 ∙ 4.2918254868914E+156 + 5 ∙ 7.8033190670752E+154 + 6 ∙ 1.4187852849228E+153 + 4 ∙ 2.5796096089505E+151 + 8 ∙ 4.6901992890009E+149 + 3 ∙ 8.5276350709107E+147 + 3 ∙ 1.5504791038019E+146 + 5 ∙ 2.8190529160035E+144 + 6 ∙ 5.12555075637E+142 + 4 ∙ 9.3191831934001E+140 + 3 ∙ 1.6943969442546E+139 + 8 ∙ 3.0807217168265E+137 + 5 ∙ 5.6013122124118E+135 + 6 ∙ 1.0184204022567E+134 + 8 ∙ 1.8516734586485E+132 + 4 ∙ 3.3666790157246E+130 + 3 ∙ 6.1212345740447E+128 + 5 ∙ 1.1129517407354E+127 + 6 ∙ 2.0235486195189E+125 + 4 ∙ 3.6791793082162E+123 + 3 ∙ 6.6894169240294E+121 + 8 ∙ 1.2162576225508E+120 + 5 ∙ 2.2113774955469E+118 + 6 ∙ 4.0206863555399E+116 + 4 ∙ 7.3103388282543E+114 + 5 ∙ 1.3291525142281E+113 + 6 ∙ 2.4166409349601E+111 + 8 ∙ 4.3938926090184E+109 + 4 ∙ 7.9888956527606E+107 + 3 ∙ 1.4525264823201E+106 + 6 ∙ 2.640957240582E+104 + 5 ∙ 4.8017404374219E+102 + 8 ∙ 8.7304371589489E+100 + 4 ∙ 1.587352210718E+99 + 5 ∙ 2.8860949285781E+97 + 6 ∙ 5.2474453246875E+95 + 8 ∙ 9.54080968125E+93 + 7 ∙ 1.7346926693182E+92 + 4 ∙ 3.1539866714876E+90 + 3 ∙ 5.7345212208866E+88 + 5 ∙ 1.0426402219794E+87 + 6 ∙ 1.895709494508E+85 + 6 ∙ 3.446744535469E+83 + 6 ∙ 6.2668082463073E+81 + 6 ∙ 1.1394196811468E+80 + 6 ∙ 2.0716721475396E+78 + 3 ∙ 3.7666766318902E+76 + 7 ∙ 6.8485029670731E+74 + 5 ∙ 1.2451823576496E+73 + 6 ∙ 2.2639679229994E+71 + 8 ∙ 4.1163053145443E+69 + 4 ∙ 7.4841914809896E+67 + 3 ∙ 1.3607620874527E+66 + 5 ∙ 2.4741128862776E+64 + 6 ∙ 4.4983870659592E+62 + 4 ∙ 8.1788855744713E+60 + 3 ∙ 1.4870701044493E+59 + 7 ∙ 2.7037638262715E+57 + 5 ∙ 4.9159342295845E+55 + 6 ∙ 8.9380622356083E+53 + 4 ∙ 1.625102224656E+52 + 8 ∙ 2.9547313175564E+50 + 3 ∙ 5.3722387591935E+48 + 5 ∙ 9.7677068348973E+46 + 6 ∙ 1.7759466972541E+45 + 8 ∙ 3.2289939950074E+43 + 7 ∙ 5.8708981727407E+41 + 4 ∙ 1.0674360314074E+40 + 5 ∙ 1.9407927843771E+38 + 6 ∙ 3.5287141534129E+36 + 8 ∙ 6.4158439152962E+34 + 7 ∙ 1.1665170755084E+33 + 4 ∙ 2.120940137288E+31 + 5 ∙ 3.8562547950691E+29 + 6 ∙ 7.011372354671E+27 + 7 ∙ 1.2747949735766E+26 + 4 ∙ 2.3178090428665E+24 + 3 ∙ 4.2141982597572E+22 + 6 ∙ 7.662178654104E+20 + 5 ∙ 1.3931233916553E+19 + 8 ∙ 253295162119140625 + 7 ∙ 4605366583984375 + 4 ∙ 83733937890625 + 6 ∙ 1522435234375 + 5 ∙ 27680640625 + 4 ∙ 503284375 + 3 ∙ 9150625 + 8 ∙ 166375 + 6 ∙ 3025 + 5 ∙ 55 + 4 ∙ 1 = INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + INF + 1.811656516242E+307 + 2.1959472924146E+305 + 4.6580700142127E+303 + 6.0494415768997E+301 + 8.7991877482177E+299 + 3.1997046357155E+298 + 4.3632335941575E+296 + 9.2553439876069E+294 + 1.2019927256632E+293 + 1.7483530555102E+291 + 6.3576474745824E+289 + 1.0114439164108E+288 + 1.5762762333675E+286 + 4.2989351819114E+284 + 4.3423587696075E+282 + 6.3161582103382E+280 + 2.0096867032894E+279 + 3.1319792778537E+277 + 8.5417616668736E+275 + 1.3804867340402E+274 + 1.5687349250457E+272 + 2.2817962546119E+270 + 7.2602608101287E+268 + 1.1314692171629E+267 + 1.7143472987317E+265 + 4.3637931240443E+263 + 6.8007165569521E+261 + 1.0304115995382E+260 + 2.2481707626288E+258 + 4.7688470722429E+256 + 1.1147954194854E+255 + 1.1260559792781E+253 + 3.2757992124455E+251 + 5.2114987470724E+249 + 6.7681801910031E+247 + 9.8446257323681E+245 + 2.6848979270095E+244 + 3.2544217297085E+242 + 1.0354978230891E+241 + 1.3448023676481E+239 + 2.9341142566868E+237 + 3.5565021293174E+235 + 1.29327350157E+234 + 1.4696289790568E+232 + 4.8096948405494E+230 + 5.8299331400599E+228 + 7.066585624315E+226 + 9.6362531240659E+224 + 4.0881073859674E+223 + 5.3092303713862E+221 + 1.1583775355752E+220 + 1.4040939825154E+218 + 1.9146736125209E+216 + 8.1228577500888E+214 + 1.2658999091048E+213 + 1.9180301653102E+211 + 5.5797241172661E+209 + 8.8768338229234E+207 + 9.222684491349E+205 + 2.5152775885497E+204 + 3.8110266493178E+202 + 1.1086622979833E+201 + 1.7637809286099E+199 + 1.8324996660882E+197 + 2.4988631810293E+195 + 9.086775203743E+193 + 1.3767841217792E+192 + 4.0051901724487E+190 + 6.3718934561684E+188 + 6.6201490453698E+186 + 9.0274759709588E+184 + 3.2827185348941E+183 + 4.9738159619608E+181 + 1.4469282798431E+180 + 2.3019313542959E+178 + 2.3916169914762E+176 + 3.2612958974676E+174 + 1.1859257808973E+173 + 1.7968572437838E+171 + 5.2272210728256E+169 + 4.7520191571142E+167 + 6.4800261233376E+165 + 1.9636442797993E+164 + 4.2843147922893E+162 + 1.0386217678277E+161 + 9.442016071161E+158 + 3.0042778408239E+157 + 3.9016595335376E+155 + 8.5127117095366E+153 + 1.0318438435802E+152 + 3.7521594312007E+150 + 2.5582905212732E+148 + 4.6514373114058E+146 + 1.4095264580018E+145 + 3.075330453822E+143 + 3.72767327736E+141 + 5.0831908327637E+139 + 2.4645773734612E+138 + 2.8006561062059E+136 + 6.1105224135401E+134 + 1.4813387669188E+133 + 1.3466716062898E+131 + 1.8363703722134E+129 + 5.564758703677E+127 + 1.2141291717113E+126 + 1.4716717232865E+124 + 2.0068250772088E+122 + 9.7300609804065E+120 + 1.1056887477735E+119 + 2.4124118133239E+117 + 2.9241355313017E+115 + 6.6457625711403E+113 + 1.4499845609761E+112 + 3.5151140872147E+110 + 3.1955582611043E+108 + 4.3575794469604E+106 + 1.5845743443492E+105 + 2.4008702187109E+103 + 6.9843497271591E+101 + 6.3494088428719E+99 + 1.4430474642891E+98 + 3.1484671948125E+96 + 7.632647745E+94 + 1.2142848685227E+93 + 1.261594668595E+91 + 1.720356366266E+89 + 5.2132011098969E+87 + 1.1374256967048E+86 + 2.0680467212814E+84 + 3.7600849477844E+82 + 6.8365180868807E+80 + 1.2430032885238E+79 + 1.1300029895671E+77 + 4.7939520769511E+75 + 6.2259117882482E+73 + 1.3583807537996E+72 + 3.2930442516354E+70 + 2.9936765923958E+68 + 4.082286262358E+66 + 1.2370564431388E+65 + 2.6990322395755E+63 + 3.2715542297885E+61 + 4.461210313348E+59 + 1.89263467839E+58 + 2.4579671147923E+56 + 5.362837341365E+54 + 6.5004088986242E+52 + 2.3637850540452E+51 + 1.6116716277581E+49 + 4.8838534174487E+47 + 1.0655680183524E+46 + 2.5831951960059E+44 + 4.1096287209185E+42 + 4.2697441256296E+40 + 9.7039639218855E+38 + 2.1172284920477E+37 + 5.1326751322369E+35 + 8.1656195285588E+33 + 8.483760549152E+31 + 1.9281273975345E+30 + 4.2068234128026E+28 + 8.9235648150359E+26 + 9.2712361714658E+24 + 1.2642594779272E+23 + 4.5973071924624E+21 + 6.9656169582764E+19 + 2026361296953125000 + 32237566087890625 + 334935751562500 + 9134611406250 + 138403203125 + 2013137500 + 27451875 + 1331000 + 18150 + 275 + 4 = INF10
Таким образом:
675768578567587685768576979864796754867548769547698547657656795875464756485964375643765874658743658743658743658435684756483356438568435643856456843658456874356666637568435643756483568745687456743658746543865455 = INF10.