[Number Theory]
Problem: Compute the least integer greater than 2023 , the sum of whose digits is 17 .

Solution: A candidate for desired number is $\underline{2} \underline{0} \underline{X} \underline{Y}$, where $X$ and $Y$ are digits and $X+Y=15$. To minimize this number, take $Y=9$. Then $X=6$, and the desired number is 2069 .

Final answer: 2069