Must I Do All This?!

Algebra Level 5

Let \(\text{S}\) be the sum of all possible positive integers \(\text{N}\), for which there exists an arithmetic progression of positive integers starting with 1 and common difference \(N\), which contains the term 2015.

Determine the value of \(S \text{(mod 1000)}\).

[Based off an old problem, but nothing like it.]

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