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Digit Sum Divisibility (Posted on 2021-06-11) Difficulty: 3 of 5
Let S(n) be the sum of the digits of a natural number n, e.g. S(168) = 15.

Call a number n "special" if it is evenly divisible by S(n), e.g. 36 is special because S(36) = 9 and 9 divides 36.

Prove that there cannot be a sequence of 22 consecutive numbers that are all special.

Bonus: Prove that there cannot be a sequence of 21 consecutive special numbers.

No Solution Yet Submitted by tomarken    
Rating: 5.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionMath Man2021-06-16 20:22:54
Some ThoughtsSolution, not bonusJer2021-06-11 11:05:35
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