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ways to write 2000 as a sum of 3 positive integers

Source: Nordic Mathematical Contest 2000 #1

October 3, 2017
combinatoricsIntegersSum

Problem Statement

In how many ways can the number 20002000 be written as a sum of three positive, not necessarily different integers? (Sums like 1+2+31 + 2 + 3 and 3+1+23 + 1 + 2 etc. are the same.)
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