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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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.
Last edited by chiph588@; Feb 5th 2011 at 10:45 AM.
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