a problem from IUMO 09
What's your new problem? I couldn't get it.
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Re: a problem from IUMO 09
See the last problem carefully. It said there are powers of $2$ with digits only $1$ and $2$. You just proved that last $n$ digits have digits $1$ and $2$ according to your claim, right?
One one thing is neutral in the universe, that is $0$.