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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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closed as off topic by Anton Geraschenko Feb 3 '10 at 22:45

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question.

Prime factorization. Inappropriate for MO. –  Boris Bukh Feb 3 '10 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 '10 at 22:36
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 '10 at 22:45
Can you give us some motivation? –  Randy Brown Feb 3 '10 at 22:45

1 Answer 1

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

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