Counting Up = Counting Down

Number Theory Level 4

Hansel has to count upwards from 1, increasing the value by \(n \) each second.
Gretel has to count downwards from 1000, decreasing the value by \(m\) each second.

If \(m\) and \(n\) are both positive integers, at how many (distinct) seconds can they possibly say the same number at the same time?

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