Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.0 AIME, harder Prove it Netherlands

The *digit sum* of a number is obtained by adding all digits of the number. For example, the digit sum of $1303$ is $1 + 3 + 0 + 3 = 7$ . Find the smallest positive integer $n$ for which both the digit sum of $n$ and the digit sum of $n + 1$ are divisible by $5$ .

Solution

$49999$

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