This seems a simple question but I am unsure as to why I cannot find a number n where(adsbygoogle = window.adsbygoogle || []).push({});

2^n mod 3 = 0

I am trying to solve a puzzle (I'm not a student) and I think that this may be the key to the puzzle. At first it seemed pretty plausible that there would be a 2^n which was divisible by 3 but having tried the first 64 n's it is now seeming that there may not be. I cannot understand why though. Can anybody let me know if this number exists and if not why not?

(In case you need an example)

2^2 = 4, 4mod3 = 1

2^3 = 8, 8mod3 = 2

etc

Thanks,

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# Does (2^n) mod 3 = 0 exist?

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