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Can we work out the sum of the digits of the number $3^{1000}$ without any program?

I just means the way of pure mathematics.

I'm interested in learning more way to solve this problem.Let's solve it together.

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We have been asked not to discuss Project Euler problems. –  Gerry Myerson Jul 15 '12 at 8:45
    
@GerryMyerson Oh, I didn't knew that –  Norbert Jul 15 '12 at 8:45
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@GerryMyerson We should disregard those people. People who wish to do these problems earnestly will try them on their own before (if ever) looking up the answer. Your reasoning would imply that we should consider request to not answer certain questions because they may be exercises from textbooks which could potentially be someone's homework. –  William Jul 15 '12 at 9:16
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Please see meta.math.stackexchange.com/questions/1090/… and some of the links and discussion there. –  Gerry Myerson Jul 15 '12 at 10:59
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I think this is an interesting question, and pointedly different from the PE way of doing things. However, I don't think SE is really a social site, and I think if you want to make friends there are better places to go. –  Ben Millwood Jul 15 '12 at 11:16
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