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S(n)-(5n)=2013

Source: Canadian Repêchage 2013: Problem 5

May 20, 2014
number theory proposednumber theory

Problem Statement

For each positive integer kk, let S(k)S(k) be the sum of its digits. For example, S(21)=3S(21) = 3 and S(105)=6S(105) = 6. Let nn be the smallest integer for which S(n)−S(5n)=2013S(n) - S(5n) = 2013. Determine the number of digits in nn.
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