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Best Answer Sid Kemp says
Partial answer - no sum of digits of a power of 2 is divisible by 3. All are divisible by primes higher than three, and (if even) two itself).
Thanks, Paxwill. I didn't know the right terms such as "divisibility rule" to research this further. I guessed modular math would be part of it. Is there a name for the branch of math from which divisibility rules are developed?
I wanted to comment on Sid's answer since he solved it first, but the system won't let me for some reason. Anyway, this falls under the umbrella of number theory. Good work the both of you, thanks for taking the time to solve it.
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