Let p>5 be a prime. Prove that p divides infinitely many numbers of the (base ten) form:

1, 11, 111, 1111, 11111, 111111, ...

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- February 28th 2010, 12:11 PMNikoBellicProve that p divides infinitely many numbers...
Let p>5 be a prime. Prove that p divides infinitely many numbers of the (base ten) form:

1, 11, 111, 1111, 11111, 111111, ... - February 28th 2010, 05:55 PMchiph588@
Let .

Define .

Note , since i.e. .

Thus .

Now let

and define .

Observe if , then .

But since .

Hence .

Since is not a finite set, we are done.