divisor polynomials

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Problem

for each positive integer n from 1 to 200, print the monic polynomial (leading coefficient is 1) whose roots are precisely the divisors of n, including n

Options

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rejudge feature is enabled

now post-mortem time, all source codes will be revealed

Sample input:_

*NOTHING*

Sample output:

-1+x
2-3x+x^2
3-4x+x^2
-8+14x-7x^2+x^3
5-6x+x^2
36-72x+47x^2-12x^3+x^4
7-8x+x^2
64-120x+70x^2-15x^3+x^4
-27+39x-13x^2+x^3
100-180x+97x^2-18x^3+x^4
11-12x+x^2
1728-4032x+3444x^2-1400x^3+287x^4-28x^5+x^6
13-14x+x^2
196-336x+163x^2-24x^3+x^4
225-360x+158x^2-24x^3+x^4
-1024+1984x-1240x^2+310x^3-31x^4+x^5
17-18x+x^2
5832-12636x+9594x^2-3285x^3+533x^4-39x^5+x^6
19-20x+x^2
8000-16800x+12180x^2-3948x^3+609x^4-42x^5+x^6
441-672x+262x^2-32x^3+x^4
484-792x+343x^2-36x^3+x^4
23-24x+x^2
331776-829440x+792000x^2-383040x^3+103348x^4-15960x^5+1375x^6-60x^7+x^8
-125+155x-31x^2+x^3
676-1092x+457x^2-42x^3+x^4
729-1080x+390x^2-40x^3+x^4
21952-43904x+29204x^2-8240x^3+1043x^4-56x^5+x^6
29-30x+x^2
810000-1944000x+1747800x^2-779760x^3+190081x^4-25992x^5+1942x^6-72x^7+x^8
31-32x+x^2
32768-64512x+41664x^2-11160x^3+1302x^4-63x^5+x^6
1089-1584x+542x^2-48x^3+x^4
1156-1836x+733x^2-54x^3+x^4
1225-1680x+502x^2-48x^3+x^4
-10077696+25474176x-24766560x^2+12326040x^3-3482388x^4+580398x^5-57065x^6+3185x^7-91x^8+x^9
37-38x+x^2
1444-2280x+895x^2-60x^3+x^4
1521-2184x+718x^2-56x^3+x^4
2560000-5760000x+4712000x^2-1864800x^3+396564x^4-46620x^5+2945x^6-90x^7+x^8
41-42x+x^2
3111696-7112448x+5923512x^2-2366784x^3+497113x^4-56352x^5+3358x^6-96x^7+x^8
43-44x+x^2
85184-162624x+98868x^2-23592x^3+2247x^4-84x^5+x^6
91125-157950x+83655x^2-18612x^3+1859x^4-78x^5+x^6
2116-3312x+1267x^2-72x^3+x^4
47-48x+x^2
254803968-658243584x+661671936x^2-345692160x^3+104677824x^4-19254592x^5+2180788x^6-150040x^7+5983x^8-124x^9+x^10
-343+399x-57x^2+x^3
125000-232500x+134850x^2-29955x^3+2697x^4-93x^5+x^6
2601-3672x+1142x^2-72x^3+x^4
140608-264992x+156884x^2-35420x^3+3017x^4-98x^5+x^6
53-54x+x^2
8503056-18895680x+15017400x^2-5579280x^3+1052793x^4-103320x^5+5150x^6-120x^7+x^8
3025-3960x+1006x^2-72x^3+x^4
9834496-21073920x+15915200x^2-5604480x^3+1023828x^4-100080x^5+5075x^6-120x^7+x^8
3249-4560x+1390x^2-80x^3+x^4
3364-5220x+1945x^2-90x^3+x^4
59-60x+x^2
46656000000-130636800000x+147510720000x^2-90175680000x^3+33520208400x^4-8017571520x^5+1267844408x^6-133626192x^7+9311169x^8-417480x^9+11382x^10-168x^11+x^12
61-62x+x^2
3844-5952x+2203x^2-96x^3+x^4
250047-412776x+197379x^2-37680x^3+3133x^4-104x^5+x^6
-2097152+4161536x-2731008x^2+755904x^3-94488x^4+5334x^5-127x^6+x^7
4225-5460x+1318x^2-84x^3+x^4
18974736-41399424x+31877208x^2-11243232x^3+1953889x^4-170352x^5+7318x^6-144x^7+x^8
67-68x+x^2
314432-582624x+332724x^2-69300x^3+4893x^4-126x^5+x^6
4761-6624x+1958x^2-96x^3+x^4
24010000-49392000x+34878200x^2-11178720x^3+1835241x^4-159696x^5+7118x^6-144x^7+x^8
71-72x+x^2
139314069504-377308938240x+407004549120x^2-234871902720x^3+81507523968x^4-18022137120x^5+2612034360x^6-250307460x^7+15722902x^8-629265x^9+15145x^10-195x^11+x^12
73-74x+x^2
5476-8436x+3073x^2-114x^3+x^4
421875-697500x+332475x^2-61160x^3+4433x^4-124x^5+x^6
438976-808640x+455924x^2-92120x^3+5999x^4-140x^5+x^6
5929-7392x+1558x^2-96x^3+x^4
37015056-79724736x+60000408x^2-20350512x^3+3310993x^4-260904x^5+9862x^6-168x^7+x^8
79-80x+x^2
3276800000-7618560000x+6586880000x^2-2845056000x^3+691334720x^4-99608544x^5+8641684x^6-444540x^7+12865x^8-186x^9+x^10
-59049+88209x-32670x^2+3630x^3-121x^4+x^5
6724-10332x+3733x^2-126x^3+x^4
83-84x+x^2
351298031616-936794750976x+987677203968x^2-552172529664x^3+183657582864x^4-38428631808x^5+5195461144x^6-457483712x^7+26028569x^8-931616x^9+19838x^10-224x^11+x^12
7225-9180x+2062x^2-108x^3+x^4
7396-11352x+4087x^2-132x^3+x^4
7569-10440x+2990x^2-120x^3+x^4
59969536-122664960x+85300160x^2-26262720x^3+3945588x^4-298440x^5+11015x^6-180x^7+x^8
89-90x+x^2
531441000000-1381746600000x+1408187430000x^2-756352080000x^3+241080453900x^4-48407441940x^5+6306351777x^6-537860466x^7+29763019x^8-1037520x^9+21463x^10-234x^11+x^12
8281-10192x+2022x^2-112x^3+x^4
778688-1421952x+786324x^2-151440x^3+8547x^4-168x^5+x^6
8649-11904x+3382x^2-128x^3+x^4
8836-13536x+4843x^2-144x^3+x^4
9025-11400x+2494x^2-120x^3+x^4
782757789696-2054739197952x+2117166170112x^2-1147318566912x^3+366480543744x^4-72894560256x^5+9268646336x^6-759318336x^7+39765684x^8-1296792x^9+24927x^10-252x^11+x^12
97-98x+x^2
941192-1642284x+832314x^2-139545x^3+8493x^4-171x^5+x^6
970299-1528956x+655083x^2-102888x^3+6617x^4-156x^5+x^6
-1000000000+2170000000x-1670900000x^2+603023000x^3-112818300x^4+11281830x^5-603023x^6+16709x^7-217x^8+x^9
101-102x+x^2
108243216-229220928x+167275512x^2-53691984x^3+7904713x^4-526392x^5+16078x^6-216x^7+x^8
103-104x+x^2
116985856-236221440x+160347200x^2-47305440x^3+6634068x^4-454860x^5+14825x^6-210x^7+x^8
121550625-222264000x+131550300x^2-35300160x^3+4787686x^4-336192x^5+11932x^6-192x^7+x^8
11236-17172x+6097x^2-162x^3+x^4
107-108x+x^2
1586874322944-4114118615040x+4161735728640x^2-2198499770880x^3+678856662288x^4-129287430720x^5+15579722520x^6-1197105840x^7+58201017x^8-1745240x^9+30590x^10-280x^11+x^12
109-110x+x^2
146410000-287496000x+186315800x^2-51725520x^3+6950769x^4-470232x^5+15398x^6-216x^7+x^8
12321-16872x+4702x^2-152x^3+x^4
17623416832-39023280128x+31227334656x^2-12101447680x^3+2567988416x^4-315997824x^5+22928468x^6-964720x^7+22227x^8-248x^9+x^10
113-114x+x^2
168896016-355570560x+256671000x^2-80739360x^3+11431633x^4-708240x^5+19750x^6-240x^7+x^8
13225-16560x+3478x^2-144x^3+x^4
1560896-2825760x+1532244x^2-280380x^3+13209x^4-210x^5+x^6
1601613-2491398x+1032759x^2-151620x^3+8827x^4-182x^5+x^6
13924-21240x+7495x^2-180x^3+x^4
14161-17136x+3118x^2-144x^3+x^4
42998169600000000-128994508800000000x+160496640000000000x^2-111625039872000000x^3+49030162721280000x^4-14507747896320000x^5+3002661777600000x^6-444438718732800x^7+47604489653776x^8-3703655989440x^9+208518179000x^10-8395687440x^11+236449473x^12-4485960x^13+53750x^14-360x^15+x^16
-1331+1463x-133x^2+x^3
14884-22692x+7993x^2-186x^3+x^4
15129-20664x+5702x^2-168x^3+x^4
1906624-3444224x+1858388x^2-335552x^3+14987x^4-224x^5+x^6
15625-19500x+4030x^2-156x^3+x^4
4001504141376-9908486445312x+9400610982672x^2-4589086586112x^3+1298742514524x^4-226766279376x^5+25201856331x^6-1799732376x^7+81805399x^8-2294112x^9+37297x^10-312x^11+x^12
127-128x+x^2
268435456-534773760x+353730560x^2-99486720x^3+12850368x^4-777240x^5+21590x^6-255x^7+x^8
16641-22704x+6238x^2-176x^3+x^4
285610000-553644000x+349863800x^2-92743560x^3+11606721x^4-713412x^5+20702x^6-252x^7+x^8
131-132x+x^2
5289852801024-13465079857152x+13248312473088x^2-6728675982336x^3+1968913690128x^4-349231994496x^5+38444448824x^6-2645696928x^7+113000097x^8-2925552x^9+43638x^10-336x^11+x^12
17689-21280x+3750x^2-160x^3+x^4
17956-27336x+9583x^2-204x^3+x^4
332150625-590490000x+330601500x^2-81550800x^3+9874854x^4-604080x^5+18140x^6-240x^7+x^8
342102016-679173120x+446216000x^2-123893280x^3+15635508x^4-910980x^5+24125x^6-270x^7+x^8
137-138x+x^2
362673936-756884736x+537459768x^2-163864512x^3+21775033x^4-1187424x^5+28222x^6-288x^7+x^8
139-140x+x^2
7529536000000-18070886400000x+16441279680000x^2-7657077120000x^3+2067116528400x^4-343939263360x^5+36324566872x^6-2456709024x^7+105465129x^8-2790480x^9+42798x^10-336x^11+x^12
19881-27072x+7382x^2-192x^3+x^4
20164-30672x+10723x^2-216x^3+x^4
20449-24024x+3742x^2-168x^3+x^4
-15407021574586368+43118261767766016x-48807476862124032x^2+30117106457247744x^3-11444075422580736x^4+2856135667986432x^5-485991557835264x^6+57590665711488x^7-4799222142624x^8+281245114488x^9-11478168676x^10+319383142x^11-5836897x^12+65689x^13-403x^14+x^15
21025-26100x+5254x^2-180x^3+x^4
21316-32412x+11317x^2-222x^3+x^4
3176523-4926852x+2019339x^2-282520x^3+13737x^4-228x^5+x^6
3241792-5826464x+3106964x^2-543020x^3+20993x^4-266x^5+x^6
149-150x+x^2
11390625000000-28248750000000x+26789231250000x^2-12988998000000x^3+3602169697500x^4-602785359000x^5+62369680175x^6-4018569060x^7+160096431x^8-3848592x^9+52917x^10-372x^11+x^12
151-152x+x^2
533794816-1053542400x+684224960x^2-185774400x^3+22489908x^4-1222200x^5+29615x^6-300x^7+x^8
3581577-5477706x+2169999x^2-287820x^3+14183x^4-234x^5+x^6
562448656-1051852032x+621880952x^2-148446144x^3+16906569x^4-963936x^5+26222x^6-288x^7+x^8
24025-29760x+5926x^2-192x^3+x^4
14412774445056-36216715272192x+34931552527872x^2-17234787128832x^3+4840914418704x^4-811693611456x^5+82963346296x^6-5203164176x^7+198919889x^8-4539752x^9+58982x^10-392x^11+x^12
157-158x+x^2
24964-37920x+13195x^2-240x^3+x^4
25281-34344x+9278x^2-216x^3+x^4
16777216000000-39636172800000x+35190865920000x^2-15838986240000x^3+4092471398400x^4-645577067520x^5+64061597248x^6-4034856672x^7+159862164x^8-3866940x^9+53697x^10-378x^11+x^12
25921-30912x+5182x^2-192x^3+x^4
111577100832-250015355568x+201658476096x^2-76879436040x^3+15185532186x^4-1617173019x^5+93737853x^6-2929410x^7+47432x^8-363x^9+x^10
163-164x+x^2
4410944-7907424x+4191348x^2-720132x^3+25557x^4-294x^5+x^6
741200625-1293732000x+697286700x^2-161710560x^3+17909974x^4-980064x^5+25612x^6-288x^7+x^8
27556-41832x+14527x^2-252x^3+x^4
167-168x+x^2
634562281237118976-1813035089248911360x+2112284804500684800x^2-1353031394729656320x^3+538531534956957696x^4-142117594792427520x^5+25828571469657600x^6-3305880253347840x^7+301558896887056x^8-19677858650880x^9+915127957400x^10-29972295360x^11+676042521x^12-10110240x^13+93950x^14-480x^15+x^16
-2197+2379x-183x^2+x^3
835210000-1591812000x+972138200x^2-241195320x^3+27044601x^4-1418796x^5+33638x^6-324x^7+x^8
5000211-7602660x+2963259x^2-377880x^3+17329x^4-260x^5+x^6
5088448-9111872x+4817204x^2-821480x^3+28007x^4-308x^5+x^6
173-174x+x^2
916636176-1896488640x+1324575000x^2-390936240x^3+48417073x^4-2246760x^5+43750x^6-360x^7+x^8
5359375-7595000x+2533475x^2-312080x^3+14477x^4-248x^5+x^6
168874213376-356938678272x+263816892416x^2-90456115200x^3+16238518208x^4-1624222656x^5+92264308x^6-2920200x^7+48391x^8-372x^9+x^10
31329-42480x+11390x^2-240x^3+x^4
31684-48060x+16645x^2-270x^3+x^4
179-180x+x^2
198359290368000000000-601689847449600000000x+760469112748800000000x^2-540292341173760000000x^3+244134778654166400000x^4-74976972765065280000x^5+16289452586095560000x^6-2567533005516024000x^7+298227263856565680x^8-25747523233207776x^9+1656818132536476x^10-79244845849260x^11+2793116012705x^12-71422965978x^13+1292013723x^14-15885240x^15+124215x^16-546x^17+x^18
181-182x+x^2
1097199376-2025598848x+1165898552x^2-263993184x^3+27909753x^4-1450512x^5+35198x^6-336x^7+x^8
33489-45384x+12142x^2-248x^3+x^4
1146228736-2242621440x+1431262400x^2-375315840x^3+42443988x^4-2039760x^5+42275x^6-360x^7+x^8
34225-42180x+8182x^2-228x^3+x^4
1196883216-2470984704x+1718660088x^2-503039232x^3+61135849x^4-2704512x^5+49678x^6-384x^7+x^8
34969-40392x+5638x^2-216x^3+x^4
6644672-11875584x+6249684x^2-1051680x^3+33243x^4-336x^5+x^6
1275989841-2160406080x+1096634700x^2-235327680x^3+24323958x^4-1245120x^5+30700x^6-320x^7+x^8
1303210000-2469240000x+1489847000x^2-360673200x^3+38713569x^4-1898280x^5+41270x^6-360x^7+x^8
191-192x+x^2
9618527719784448-25449021258596352x+26542533890801664x^2-14642299828961280x^3+4799143640825856x^4-990694694191104x^5+132920614146048x^6-11776171735040x^7+692294865344x^8-26874313536x^9+678047412x^10-10774680x^11+101727x^12-508x^13+x^14
193-194x+x^2
37636-57036x+19693x^2-294x^3+x^4
1445900625-2491398000x+1306082700x^2-288877680x^3+29739766x^4-1481424x^5+34348x^6-336x^7+x^8
-20661046784+42059988096x-28969889760x^2+8752166360x^3-1268703492x^4+90621678x^5-3189565x^6+53865x^7-399x^8+x^9
197-198x+x^2
60254729561664-142420269873024x+125656716783312x^2-55264380893568x^3+13595180644188x^4-1991810178072x^5+179553860631x^6-10059647364x^7+346780447x^8-7119504x^9+81757x^10-468x^11+x^12
199-200x+x^2
64000000000000-148800000000000x+128712000000000x^2-55707960000000x^3+13618912560000x^4-1992415260000x^5+179091187000x^6-9962076300x^7+340472814x^8-6963495x^9+80445x^10-465x^11+x^12

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