Saturday, October 1, 2016

number theory - Prove that (integer)-(the sum of it's digits) can be divided by 9

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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