- #1
basik156
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Homework Statement
Show that infinitely many of the numbers
11, 101, 1001, 10001, 100001,...
are composite
Homework Equations
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.