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MathNet 2018-part-01 — 181 problems (EN–VI) Question 25

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 25

For every positive integer $m$, we write $S(m)$ for the sum of its digits. For example, $S(2018) = 2+0+1+8=11$.
We say a positive integer $n$ is *rioplatense* if there is a positive integer $m$ such that $m + 2S(m) = n$.
Find all positive integers that are *rioplatenses*.