Brilli the Ant states that "Given **any** \(N\) integers, we can always find two distinct integers whose difference of squares is a multiple of 1000."

What is the smallest integer value of \(N\) that would make the statement true?

**Details and assumptions**

Clarification: You are given a random collection of \(N\) integers. You are not given the integers from 1 to \(N\).

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