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Omni-MATH / The product of N consecutive four-digit positive integers is divisible by 2010². What is the least possible value of N?

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problem

The product of NN consecutive four-digit positive integers is divisible by 201022010^{2}. What is the least possible value of NN?
Plain-text mathematical notation (without MathML)
The product of N consecutive four-digit positive integers is divisible by 2010². What is the least possible value of N?
Original LaTeX notation
The product of $N$ consecutive four-digit positive integers is divisible by $2010^{2}$. What is the least possible value of $N$?

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