Determine the smallest positive integer which is 2 times a square, 3 times a cube, 5 times a fifth power, 7 times a seventh power, and 11 times an eleventh power.
For example, 648 is 2 times the square of 18, and 3 times the cube of 6.
2 must be present as a factor 3*5*7*11 times.
3 must be present as a factor 2*5*7*11 times.
5 must be present as a factor 2*3*7*11 times.
7 must be present as a factor 2*3*5*11 times.
11 must be present as a factor 2*3*5*7 times.
Therefore 2^1155 * 3^770 * 5^462 * 7*330 * 11^210 is the answer.
That's:
11303917843093092340258335839271739736093007257041362263962521637934525
87615260154386921495923321070357844175260255752660843528445421262356042
68496933122301203908214540488179341595867730873730481906750316193617430
88146344952420888471863828700367828685521146246730579995869427042274623
79025997405442025546265340023979310642104745037011917956989344194904117
68852077090297783421577695515997870405085898765857785050387672997585080
30375773754086792304152388658010359356816862255231296013654897242091095
36510997590687686420562349039683368904555644322591823802884390928610940
37812554152295403929446576367583782651529846431461356239508703341119852
21220157942969573693907988556191557424431773015690081497310509235587381
45657015960803490801606287504794726717973451408306485562979323625782412
69899731610370048000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000
That's 1261 digits long.
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Posted by Charlie
on 2023-10-12 07:56:47 |
solution
