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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

too small

| Comment 2 of 4 |

(In reply to solution by Charlie)

770 is not 1 more than a multiple of 3 and 462 is not 1 more than a multiple of 5.

I make the answer to be 2^1155 * 3^1540 * 5^1386 * 7^330 * 11^210.

Posted by xdog on 2023-10-12 10:33:48

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