(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that infinitely many of the numbers

11, 101, 1001, 10001, 100001,...

are composite

2. Relevant equations

3. The attempt at a solution

So by inspecting these numbers, I notice that 11, 1001, 100001 are all divisible by 11.

The numbers can be represented at 10[itex]^{n}[/itex]+1

and when n=2k+1 where k is an integer, this number is divisible by 11, thus having a proper divisor less than √n and thus being composite.

So I know this, but I don't think I've really shown that the number is divisible by 11, I have just noticed this fact. I attempted a solution by induction, but something tells me there is a better way to show this.

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# Homework Help: Showing that a series of numbers has an infinite amount of composites

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