A problem by Aryan Gaikwad

Level pending

There are exactly three different pairs of positive integers that add to make six.

\(1\quad +\quad 5\quad =\quad 6\)

\(2\quad +\quad 4\quad =\quad 6\)

\(3\quad +\quad 3\quad =\quad 6\)

How many different pairs of positive integers add to make one-thousand?

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