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Equal digit sum (Posted on 2012-11-22) Difficulty: 5 of 5
Find all integers n such that S(n) = S(2n) = ... = S(n*n), where S is the sum of the base-10 digits.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts The first answer (spoiler) | Comment 1 of 4
Well, I'm always willing to go for the easy answer.

The obvious answer is 9.

S(9)=S(18)=S(27)=S(36)=S(45)=S(54)=S(63)=S(72)=S(81)

Arguably 0 and 1 work also, but I think the form of the problem implies that N >=2.

If there are any larger answers, they must obviously be a multiple of 9, but 18 doesn't work, so I'm going to stop looking.



  Posted by Steve Herman on 2012-11-22 12:01:25
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