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Can anyone please help me on the following proof:

Prove that there exist infinitely many positive integers $n$ such that $2^n$ ends with $n$ in decimal notation, i.e. $2n = \ldots n$.

  • 0
    To clarify, you are trying to show there are infinitely many $n\in\mathbb{Z}$ so that $2^n-n\equiv0\pmod{10^{\lfloor\log_{10}(n)\rfloor+1}}$. Correct?2012-12-09
  • 0
    Yes, but isn't this more difficult to prove2012-12-09
  • 5
    Since it is only a mathematical statement of your problem, it don't see how it could be more difficult.2012-12-09
  • 1
    BTW, see http://oeis.org/A064541.2012-12-09
  • 0
    Why the edit?? It's now a totally different question!2012-12-12
  • 1
    I changed your question back to the question to which the answerers provided and directed their answers. If you want to ask a different question, I encourage you to ask a different question *but* in a different post.2012-12-14

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