The sum of the digits of a natural number n is denoted by S(n).Prove that S(8n)≥1/8*S(n)

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