perplexus.info :: Numbers : Multiples of Powers

Multiples of Powers (Posted on 2023-10-12)

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.

Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Solution: (Hide)

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.
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(2): solution	Charlie	2023-10-15 22:21:45
re: solution	Math Man	2023-10-12 13:53:33
too small	xdog	2023-10-12 10:33:48
solution	Charlie	2023-10-12 07:56:47

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