perplexus.info :: Numbers : Higher Powers of Eleven

Higher Powers of Eleven (Posted on 2017-05-24)

Let N(x) be the number 122....221 where the digit 2 occurs x times.

Twice in the past we have determined the highest power of 11 that divides N(2001) is 11^3.

What is the smallest x for N(x) to be a multiple of 11^3? What about multiples of 11^4 and 11^5?

Submitted by Brian Smith

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Solution: (Hide)

The smallest x for N(x) to be a multiple of 11^3, 11^4, and 11^5 are 21, 241, and 2661.

I wrote a full solution in this post.

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

Subject	Author	Date
re: Analytic Solution	Charlie	2017-05-26 15:45:40
Analytic Solution	Brian Smith	2017-05-26 11:36:24
Closed form	broll	2017-05-26 00:06:45
computer solution	Charlie	2017-05-24 11:32:24

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