A problem by Aryan Gaikwad

Level pending

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

1+5=61\quad +\quad 5\quad =\quad 6

2+4=62\quad +\quad 4\quad =\quad 6

3+3=63\quad +\quad 3\quad =\quad 6

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

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