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For example the first cases are:

$2^3= 8 = 3+5$

$2^4= 16 = 3+13$

and so on ...

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    Ever heard of Goldbach's Conjecture? http://en.wikipedia.org/wiki/Goldbach%27s_conjecture2012-05-31
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    This is a special case of Goldbach's conjecture, and I think it is also open but don't have a reference. By the way, $2^2=2+2$ works.2012-05-31
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    Yes, I know that is a special case of Goldbach conjecture. And I dont have a reference too. So, i dont know if is open or not. Is a strong restriccion. And i exclude the 2. for these reason i start with 8.2012-05-31

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