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,

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**