# Solution: 2018-09 Sum of digits

For a positive integer $$n$$, let $$S(n)$$ be the sum of all decimal digits in $$n$$, i.e., if $$n = n_1 n_2 \dots n_m$$ is the decimal expansion of $$n$$, then $$S(n) = n_1 + n_2 + \dots + n_m$$. Find all positive integers $$n$$ and $$r$$ such that $$(S(n))^r = S(n^r)$$.

The best solution was submitted by Lee, Jongwon (이종원, 수리과학과 2014학번). Congratulations!

Here is his solution of problem 2018-09.

Alternative solutions were submitted by 채지석 (수리과학과 2016학번, +3), 한준호 (수리과학과 2015학번, +3), 이본우 (수리과학과 2017학번, +3), 권홍 (중앙대 물리학과, +2).

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