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Inequality in sums of digits (Posted on 2012-12-17) Difficulty: 3 of 5
The sum of the digits of a natural number n is denoted by S(n).Prove that S(8n)≥1/8*S(n)

No Solution Yet Submitted by Danish Ahmed Khan    
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quick observation Comment 1 of 1
Strict equality occurs when n = 125... where the dots stand for any number of zeros (including 0) since S(8 * 125...) = S(1...) = 1 and 1/8 * S(125...) = 1/8 * 8 = 1  
  Posted by xdog on 2012-12-17 10:44:38
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