MathDB
sum of digits

Source: Ireland 1996

July 1, 2009
number theory proposednumber theory

Problem Statement

Let S(n) S(n) denote the sum of the digits of a natural number n n (in base 10 10). Prove that for every n n, S(2n)≤2S(n)≤10S(2n) S(2n) \le 2S(n) \le 10S(2n). Prove also that there is a positive integer n n with S(n)\equal{}1996S(3n).
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