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How to prove this:

  1. Choose whichever integer you like
  2. Subtract from it the sum of it's digits
  3. The result can always be divided by 9

For example:

  1. I choose 123.
  2. The sum of it's digits is 1+2+3=6.
  3. 123-6 = 117. And 117/9 = 13.
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marked as duplicate by Bill Dubuque number-theory Feb 7 '15 at 15:07

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migrated from mathematica.stackexchange.com Feb 7 '15 at 14:58

This question came from our site for users of Wolfram Mathematica.

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    $\begingroup$ Try ls = {a, b, c, d, e, f} and FromDigits[ls] - Total[ls] // Expand and see if you can generalize. $\endgroup$ – b.gatessucks Feb 7 '15 at 13:35
  • $\begingroup$ Without Mathematica this is also easy write the number in standard form (SUM(a_i * 10^i)) and do a straightforward calculation. $\endgroup$ – mgamer Feb 7 '15 at 13:44
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    $\begingroup$ Indeed, I believe that this question belongs in the Mathematics section of StackExchange. $\endgroup$ – bbgodfrey Feb 7 '15 at 14:00