Moka asked me a problem and wanted me to post the solution on my blog. Here’s the problem for you, Mokashi:

** Question:** Prove that given any natural number, one can always append some digits in its end to get a power of 2. For example, etc. (Be wise and generalize.)

** Answer:** The given problem reduces to the following:

Given an integer , prove that there exists such that and is a power of 2.

Let be a function.

Need to show that there exists an integer such that the following inequality holds:

Now there exists an integer if the length of the interval

if and only if

** Remark:** The same proof goes through if 2 is replaced by any prime less than 10.

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