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Omni-MATH / We call a positive integer N [i]contagious[/i] if there are 1000 consecutive non-negative integers such that the sum of all their digits is N. Find all contagious positive integers…

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problem

We call a positive integer NN [i]contagious[/i] if there are 10001000 consecutive non-negative integers such that the sum of all their digits is NN. Find all contagious positive integers.
Plain-text mathematical notation (without MathML)
We call a positive integer N [i]contagious[/i] if there are 1000 consecutive non-negative integers such that the sum of all their digits is N. Find all contagious positive integers.
Original LaTeX notation
We call a positive integer $N$ [i]contagious[/i] if there are $1000$ consecutive non-negative integers such that the sum of all their digits is $N$. Find all contagious positive integers.

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