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Seems like this should be easy, but I couldn't find a single power of 2 that is divisible by 3, unless I am doing it wrong, or there is some special rule that I am overlooking.

I even wrote a C# script to try every power of 2 to see if its divisible by 3. It went up until my 64 bit computer couldn't count any higher, the last power of 2 it checked was 2^1023 or 8.98846567×10^307

Then just for a test of it ran it again looking for multiples of 5, then 6, then 7, every number up until 20 (with the obvious exception of 4, 8, & 16) and none returned multiples before hitting 2^1023

I'm assuming I didnt just make some profound discovery but there is a name for this phenomenon?

p.s, I have no idea what to tag this, new to MathOverflow.

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 Prime factorization. Inappropriate for MO. – Boris Bukh Feb 3 2010 at 22:35
Unique prime factorization tells you that the only divisors of a power of 2 are themselves powers of two. en.wikipedia.org/wiki/Prime_factor – Yemon Choi Feb 3 2010 at 22:36
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 As Yemon, Boris, and Gerry said, you can completely understand this problem once you know unique prime factorization. Though this is a fine area for you to explore, Math Overflow is really meant for research level math questions, so I'm going to close this question. There's a list of a few other forums in mathoverflow.net/faq#homework that might be a better fit for this sort of question. – Anton Geraschenko♦ Feb 3 2010 at 22:45
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 Can you give us some motivation? – Randy Brown Feb 3 2010 at 22:45

closed as off topic by Anton Geraschenko♦♦ Feb 3 2010 at 22:45

1 Answer

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Congratulations, you've rediscovered (part of) the Unique Factorization Theorem, q.v.

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